Distance, Rate And Time
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Distance Formula Solve for d, r or t
1
You are shipping a container (2 TEUs) of 30,000 athletic shoes from Hong Kong to Long Beach.
When are your shoes going to arrive in Long Beach? As long as you know the distance and the rate of speed for the ship you can figure out when the shoes are expected! 2
Objective Today we are going to learn how to apply the distance formula to find distance traveled, time traveled, or rate (speed).
CA Math Content Standard Algebra and Functions 6 2.3 Solve problems involving rates, average speed, distance, and time. 4
Purpose • • •
Tests and Quizzes Next Year’s Math Class Real life applications • • •
Shipping industry Travel industry Trip/Vacation planning
5
Distance Formula
Distance = Rate ● Time
d Feet, ft Miles Yards Inches, in Meters, m Kilometers, km Centimeters, cm Nautical Mile (≈1.15 miles)
6
Distance Formula
Distance = Rate ● Time
d
= r
Miles per Hour, mph, miles hour Kilometers per hour Meters per minute Nautical Miles per Hour = Knot 7
Distance Formula
Distance = Rate ● Time
d
= r● t
Hours Seconds Week
d = rt
Days Years Minutes
Memorize!!! 8
Tell Your Neighbor •
Determine which partner will be person A and which is person B.
•
Person A: Tell your partner what r stands for and an example unit.
•
Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of r.
r = rate
mph, km per hour, … 9
Tell Your Neighbor •
Person B: Tell your partner what t stands for and an example unit.
•
Person A: Tell your partner he or she is correct, or tell your partner the correct meaning of t.
t = time
hour, week, …
10
Tell Your Neighbor •
Person A: Tell your partner what d stands for and an example unit.
•
Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of d.
d = distance
miles, kilometers, …
11
Tell Your Neighbor •
Person B: Tell your partner the distance formula.
•
Person A: Tell your partner he or she is correct, or tell your partner the correct formula.
Distance Formula distance = rate ● time
d = r●t
d = rt
12
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? 1. Write Down Formula
d = rt
13
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? • Write Down Formula • What are you trying to find AND what do you know?
d = rt Distance = ??? = d r = 65 mph t = 3 hours
14
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? • Write Down Formula • What are you trying to find AND what do you know? • Substitute known variables and solve
d = rt Distance = ??? = d r = 65 mph t = 3 hours d = 65 miles●3 hour hour d = 195 miles 15
If you are traveling for 4 hours at 55 mph, how far will you travel? Person A: Tell Your neighbor the distance formula. d = rt Person B: Correct? Tell your neighbor the rate. r = 55 mph Person A: Correct? Tell your neighbor the time. t = 4 hours Person B: Correct? Explain how to find the distance. Person A: Correct?
Substitute r and t in formula and solve 16
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 17
On Your Own Solve Using Distance Formula: You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
18
Check with your group members Teach anyone who needs help. You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
19
One person teaches
I will select one person to teach the class You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
20
Solution You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel? d = rt d = 35 miles ● 2 hour hour d = 70 miles
21
Practice The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling? 1. Write Down Formula
d = rt
22
Practice The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day day. How far is The Glory Sanye traveling? • Write Down Formula
d = rt
• What are you trying to find AND what do you know?
Distance = ??? = d r = 480 miles per day t = 15 days 23
The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling?
• Write Down Formula
d = rt
• What are you trying to find AND what do you know?
Distance = ??? =d r = 480 miles per day t = 15 days
• Substitute known variables and solve
d = 480 miles ●15 day day d = 7200 miles 24
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 25
On Your Own Solve Using Distance Formula Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
26
Check with your group members Teach anyone who needs help Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
27
One person teaches I will select one person to teach the class. Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
28
Solution Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling? d = rt d = 520 miles ● 7 day day d = 3640 miles 29
Nautical Mile
•
Distance unit used by ships Also used by aviation (air travel) Historically equal to 1 min. latitude from the equator About 1.15 miles or equal to 1.853 km Abbreviate nm
•
1 knot = 1 nm per hour
• • •
•
30
Tell Your Neighbor •
•
Person B: Tell your neighbor the abbreviation for nautical mile.
nm
Person A: Correct? Tell your neighbor how many miles is 1 nautical mile.
1.15 miles
•
Person B: Correct? Tell your neighbor who uses nautical miles.
ships and airplanes
•
Person A: Correct? Tell your neighbor what a knot is.
nautical miles per hour
•
Person B: Correct? 31
Find Rate The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling? d = rt 1.Write down the distance formula
32
Find Rate The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?
d = rt
• Write down the distance rate = ??? = r formula
d = 13,200 nm
• What are you looking for and what do you know? t = 600 hour
33
The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?
• Write down the distance d = rt rate = ??? = r formula
Solve for r
d = 13,200 nm
• What are you looking for and what do you know? t = 600 hour
13, 200 nm = r ● 600 hour 600 hour 600 hour • Substitute and solve for 22 nm/hour = r OR rate 22 knots = r 34
Tell Your Neighbor The MSC Texas is traveling back to Hong Kong, but only a third of the containers are full. It will take the MSC Texas about 15 days to travel 12,500 kilometers to Hong Kong. How fast is the MSC Texas traveling on its return trip?
Partner A: What are you trying to find? rate or speed Partner B: Correct? What is the time? 15 days Partner A: Correct? What is the distance? 12,500 km Partner B: Correct? Explain how you would solve for the rate. Substitute distance and time and solve for r 35
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 36
On Your Own Solve Using Distance Formula: The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
37
Check with your group members
Teach anyone who needs help The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
38
One person teaches
I will select one person to teach the class The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
39
Solution The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip? d = rt 13,200 nm = r ● 550 hour 13,200 nm = r ● 550 hour 550 hour 550 hour 24 nm/hour = r OR 24 knots = r 40
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
d = rt
41
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph mph, how long will it take to reach Sacramento?
• Write down the distance formula
d = rt
time = ??? = t d = 375 miles
• What are you trying to miles r = 30 mph = 30 hour find AND What do you know 42
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
• Write down the distance formula
d = rt time = ??? = t
Solve for t
d = 375 miles
• What are you trying to miles r = 30 mph = 30 hour find AND What do miles 375 miles = 30 hour ● t you know • Substitute and solve for t
miles 30 hour
30miles hour
43
Find Time A cargo train is traveling to Sacramento, CA from Los milesAngeles,miles = miles ÷ about 375 miles by train. If the train travels at an average speed miles hour of 30 mph, how long will it take to reach Sacramento? hour
1.Write down the distance formula 2.What are you trying to find AND What do you know 3.Substitute and solve for t
d = rt
time = ??? = t d = 375 miles
= miles •
hour miles
= hour
r = 30 mph 375 miles = 30 30 miles hour
12.5 hours = t
miles ●t hour 30 miles hour
OR
12 ½ hours 44
Tell Your Neighbor The new speed trains that the State of California is looking to buy can travel 100 mph. How long would a trip from LA to Sacramento, about 375 miles, take in the new trains?
Partner B: What are you trying to find? time Partner A: Correct? What is the rate? 100 mph Partner B: Correct? What is the distance? 375 miles Partner A: Correct? Explain how you would solve for the time. Substitute distance and rate and solve for t Partner B: Correct? 45
Time to Practice •
I will give you a couple problems.
•
First, you will solve them on your own.
•
Second, you will check your solutions with your group members.
•
Third, I will select one person at random to teach the class how to solve each problem.
•
Be sure to refer to your notes for the 3 steps. 46
Alameda Corridor
Click the picture to see 4 minute clip
47
On Your Own Solve Using Distance Formula
•
In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
• Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? 48
Check with your group members Teach anyone who needs help
• In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street? •
Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? 49
One person teaches I will select one person to teach the class 1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
50
Solution 1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street? d =rt 20 miles = 10 miles/hour ● t 20 miles = 10 miles/hour ● t 10 miles/hour 10 miles/hour 2 hours = t 51
One person teaches
I will select one person to teach the class 2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
52
Solution 2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? d =rt 20 miles = 40 miles/hour ● t 20 miles = 40 miles/hour ● t 40miles/hour 40 miles/hour 0.5 hour = t
OR
½ hour = t 53
Closure
Summarize in your notes the steps for applying the distance formula to find: 2. Distance 3. Rate 4. Time 54
1
You are shipping a container (2 TEUs) of 30,000 athletic shoes from Hong Kong to Long Beach.
When are your shoes going to arrive in Long Beach? As long as you know the distance and the rate of speed for the ship you can figure out when the shoes are expected! 2
Objective Today we are going to learn how to apply the distance formula to find distance traveled, time traveled, or rate (speed).
CA Math Content Standard Algebra and Functions 6 2.3 Solve problems involving rates, average speed, distance, and time. 4
Purpose • • •
Tests and Quizzes Next Year’s Math Class Real life applications • • •
Shipping industry Travel industry Trip/Vacation planning
5
Distance Formula
Distance = Rate ● Time
d Feet, ft Miles Yards Inches, in Meters, m Kilometers, km Centimeters, cm Nautical Mile (≈1.15 miles)
6
Distance Formula
Distance = Rate ● Time
d
= r
Miles per Hour, mph, miles hour Kilometers per hour Meters per minute Nautical Miles per Hour = Knot 7
Distance Formula
Distance = Rate ● Time
d
= r● t
Hours Seconds Week
d = rt
Days Years Minutes
Memorize!!! 8
Tell Your Neighbor •
Determine which partner will be person A and which is person B.
•
Person A: Tell your partner what r stands for and an example unit.
•
Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of r.
r = rate
mph, km per hour, … 9
Tell Your Neighbor •
Person B: Tell your partner what t stands for and an example unit.
•
Person A: Tell your partner he or she is correct, or tell your partner the correct meaning of t.
t = time
hour, week, …
10
Tell Your Neighbor •
Person A: Tell your partner what d stands for and an example unit.
•
Person B: Tell your partner he or she is correct, or tell your partner the correct meaning of d.
d = distance
miles, kilometers, …
11
Tell Your Neighbor •
Person B: Tell your partner the distance formula.
•
Person A: Tell your partner he or she is correct, or tell your partner the correct formula.
Distance Formula distance = rate ● time
d = r●t
d = rt
12
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? 1. Write Down Formula
d = rt
13
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? • Write Down Formula • What are you trying to find AND what do you know?
d = rt Distance = ??? = d r = 65 mph t = 3 hours
14
Find Distance If you are traveling for 3 hours at 65 mph, how far will you have gone? • Write Down Formula • What are you trying to find AND what do you know? • Substitute known variables and solve
d = rt Distance = ??? = d r = 65 mph t = 3 hours d = 65 miles●3 hour hour d = 195 miles 15
If you are traveling for 4 hours at 55 mph, how far will you travel? Person A: Tell Your neighbor the distance formula. d = rt Person B: Correct? Tell your neighbor the rate. r = 55 mph Person A: Correct? Tell your neighbor the time. t = 4 hours Person B: Correct? Explain how to find the distance. Person A: Correct?
Substitute r and t in formula and solve 16
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 17
On Your Own Solve Using Distance Formula: You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
18
Check with your group members Teach anyone who needs help. You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
19
One person teaches
I will select one person to teach the class You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel?
20
Solution You traveled for 2 hours to get to your job at the Port or Long Beach at a rate of 35 mph, how far did you travel? d = rt d = 35 miles ● 2 hour hour d = 70 miles
21
Practice The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling? 1. Write Down Formula
d = rt
22
Practice The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day day. How far is The Glory Sanye traveling? • Write Down Formula
d = rt
• What are you trying to find AND what do you know?
Distance = ??? = d r = 480 miles per day t = 15 days 23
The Glory Sanye, an oil tanker, is traveling for 15 days from the Port of Long Beach to the Quigdoa Oil Port in the Jiao Zhou Gulf in China at a rate of 480 miles per day. How far is The Glory Sanye traveling?
• Write Down Formula
d = rt
• What are you trying to find AND what do you know?
Distance = ??? =d r = 480 miles per day t = 15 days
• Substitute known variables and solve
d = 480 miles ●15 day day d = 7200 miles 24
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 25
On Your Own Solve Using Distance Formula Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
26
Check with your group members Teach anyone who needs help Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
27
One person teaches I will select one person to teach the class. Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling?
28
Solution Now, the Gloria Sanye is traveling empty at a rate of 520 miles per day from the Quigdoa Port in China to Dubai in the United Arab Emirates. If it only takes 7 days to get to Dubai, how far is the Gloria Sanye traveling? d = rt d = 520 miles ● 7 day day d = 3640 miles 29
Nautical Mile
•
Distance unit used by ships Also used by aviation (air travel) Historically equal to 1 min. latitude from the equator About 1.15 miles or equal to 1.853 km Abbreviate nm
•
1 knot = 1 nm per hour
• • •
•
30
Tell Your Neighbor •
•
Person B: Tell your neighbor the abbreviation for nautical mile.
nm
Person A: Correct? Tell your neighbor how many miles is 1 nautical mile.
1.15 miles
•
Person B: Correct? Tell your neighbor who uses nautical miles.
ships and airplanes
•
Person A: Correct? Tell your neighbor what a knot is.
nautical miles per hour
•
Person B: Correct? 31
Find Rate The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling? d = rt 1.Write down the distance formula
32
Find Rate The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?
d = rt
• Write down the distance rate = ??? = r formula
d = 13,200 nm
• What are you looking for and what do you know? t = 600 hour
33
The MSC Texas is traveling from Hong Kong to Long Beach about 13,200 nautical miles. It is full of containers, about 8,200 TEUs. The MSC Texas will take about 600 hours (about 25 days). How fast is the MSC Texas traveling?
• Write down the distance d = rt rate = ??? = r formula
Solve for r
d = 13,200 nm
• What are you looking for and what do you know? t = 600 hour
13, 200 nm = r ● 600 hour 600 hour 600 hour • Substitute and solve for 22 nm/hour = r OR rate 22 knots = r 34
Tell Your Neighbor The MSC Texas is traveling back to Hong Kong, but only a third of the containers are full. It will take the MSC Texas about 15 days to travel 12,500 kilometers to Hong Kong. How fast is the MSC Texas traveling on its return trip?
Partner A: What are you trying to find? rate or speed Partner B: Correct? What is the time? 15 days Partner A: Correct? What is the distance? 12,500 km Partner B: Correct? Explain how you would solve for the rate. Substitute distance and time and solve for r 35
Time to Practice •
I will give you a problem.
•
First, you will solve it on your own.
•
Second, you will check your solution with your group members.
•
Third, I will select one person at random to teach the class how to solve the problem.
•
Be sure to refer to your notes for the 3 steps. 36
On Your Own Solve Using Distance Formula: The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
37
Check with your group members
Teach anyone who needs help The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
38
One person teaches
I will select one person to teach the class The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?
39
Solution The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip? d = rt 13,200 nm = r ● 550 hour 13,200 nm = r ● 550 hour 550 hour 550 hour 24 nm/hour = r OR 24 knots = r 40
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
1.Write down the distance formula
d = rt
41
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph mph, how long will it take to reach Sacramento?
• Write down the distance formula
d = rt
time = ??? = t d = 375 miles
• What are you trying to miles r = 30 mph = 30 hour find AND What do you know 42
Find Time A cargo train is traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels at an average speed of 30 mph, how long will it take to reach Sacramento?
• Write down the distance formula
d = rt time = ??? = t
Solve for t
d = 375 miles
• What are you trying to miles r = 30 mph = 30 hour find AND What do miles 375 miles = 30 hour ● t you know • Substitute and solve for t
miles 30 hour
30miles hour
43
Find Time A cargo train is traveling to Sacramento, CA from Los milesAngeles,miles = miles ÷ about 375 miles by train. If the train travels at an average speed miles hour of 30 mph, how long will it take to reach Sacramento? hour
1.Write down the distance formula 2.What are you trying to find AND What do you know 3.Substitute and solve for t
d = rt
time = ??? = t d = 375 miles
= miles •
hour miles
= hour
r = 30 mph 375 miles = 30 30 miles hour
12.5 hours = t
miles ●t hour 30 miles hour
OR
12 ½ hours 44
Tell Your Neighbor The new speed trains that the State of California is looking to buy can travel 100 mph. How long would a trip from LA to Sacramento, about 375 miles, take in the new trains?
Partner B: What are you trying to find? time Partner A: Correct? What is the rate? 100 mph Partner B: Correct? What is the distance? 375 miles Partner A: Correct? Explain how you would solve for the time. Substitute distance and rate and solve for t Partner B: Correct? 45
Time to Practice •
I will give you a couple problems.
•
First, you will solve them on your own.
•
Second, you will check your solutions with your group members.
•
Third, I will select one person at random to teach the class how to solve each problem.
•
Be sure to refer to your notes for the 3 steps. 46
Alameda Corridor
Click the picture to see 4 minute clip
47
On Your Own Solve Using Distance Formula
•
In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
• Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? 48
Check with your group members Teach anyone who needs help
• In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street? •
Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? 49
One person teaches I will select one person to teach the class 1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street?
50
Solution 1. In 2000 it trains could only travel 10 miles per hour down Alameda Street to the transfer point for cargo heading west. The distance traveled is 20 miles. How long would it take a train to travel down Alameda Street? d =rt 20 miles = 10 miles/hour ● t 20 miles = 10 miles/hour ● t 10 miles/hour 10 miles/hour 2 hours = t 51
One person teaches
I will select one person to teach the class 2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda?
52
Solution 2. Now trains can travel 40 miles per hour down the 20 mile Alameda Corridor. How long does it now take trains to travel down Alameda? d =rt 20 miles = 40 miles/hour ● t 20 miles = 40 miles/hour ● t 40miles/hour 40 miles/hour 0.5 hour = t
OR
½ hour = t 53
Closure
Summarize in your notes the steps for applying the distance formula to find: 2. Distance 3. Rate 4. Time 54
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