Converting Rates

Warm-up Wednesday, October 21, 2009 Solve a)Find the unit rate of a 12-oz bottle of orange juice that sells for $1.29 b) If you are driving 65 miles/hour,

how many feet per second are you driving?

Quick Check 2. Suppose you walk 2 miles in 35 minutes a) Find the average

walking speed. Write a rule to describe the distance d you walk as a function of the time t you walk.

b) Use the function

to find how far you would walk in an hour.

Quick Check 3. A sloth travels

0.15 miles per hour. Convert this speed to feet per minute.

4. Solve each

proportion a.

x+2 x = 14 10

Quick Check b. y − 15 = 35 y+4

7

c.

3 5 = w+6 w−4

Rates and Conversions Section 6.1 Objective: We will be able to express rates with different units.

Changing Units Change 27 feet per second to inches per second. Start by writing the rate as a division

1 ftin 324 in 27 ft 12 ⋅ = 1 sec 1 sec 11ftft

Second we multiply by fancy Next change units as needed to “ones”. Thisfinish mightthe change the multiplication and get look of the problem, butunits not its the correct value. Finally, we multiply to get our answer.

Another Example (not animated) A pool fills at 12 quarts per minute.

Find out how many gallons per hour the pool fills.

Before You Try! Please copy down (and use!!!) these

helpful English conversions: 1 mile = 5280 feet 1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts 1 pound = 16 ounces

Now You Try! Change $7.10 per hour to dollars

per minute.

Change 65 miles per hour to feet

per second.

Try some more! Convert 52 inches per minute to

yards per hour.

Change 36 miles per year to inches

per hour.

Some thoughts about why. Why would we possibly bother with this? At the 2008 Olympics Usain Bolt ran the

100 meter dash in 9.69 sec. How fast is that? (We change rates to gain meaning) If one job pays a yearly salary of $45,000

and another pays $20 an hour, which pays more assuming 40-hour work weeks? (We change rates to solve problems)

Homework Time! With lots of time to work on it, here

is your homework!!! Page 185 – 186: 1 – 37 odd

Ticket to Leave 1. Bonnie and Tim do some yard work for

their neighbor. The ratio comparing the amount of time each one works is 7:4. The neighbor pays them $88. If Bonnie worked more, how much should each of them receive? 2. If 2 tons of rock costs $15.50, then how

many tons of rock can you buy for $45?