Math 6High (Period 3)

Rates 3.8 

If two quantities a and b have different units of measure, then the rate of a per b is a/b. The units for a rate tell you which numbers goes in the numerator and which units goes in the denominator .

For example

Miles per hour = miles/hour

miles

hour

When a rate is simplified so that it has a denominator of 1, it is a unit rate.

You are traveling from San Jose,  CA to Santa Rosa, CA You travel a distance of 101 miles in 2 hours. What is your average speed in miles per hour?

Speed is one type of a unit rate. 
To find the average speed in miles per hourà divide the distance traveled by the time

Average speed = distance/time

101miles/2hours =   50.5miles/hour

You can always estimate to check that your result is reasonable.

100miles in 2 hours is 50 miles/hour so your answer makes sense

In order to compare prices at the supermarket, you can calculate unit prices. A 12 ounce box of cereal costs $ 3.72  What is the unit price of the cereal?

A unit price is another type of unit rate. Divide the cost by the weight

Unit price = Cost/weight

$3.72/12 oz

DIVIDE CAREFULLY

$0.31/1 oz

The unit price of the cereal is $0.31 per ounce.

Then we talked about a scenario involving babysitting. Suppose you babysat for one family on Saturday for 2 ½ hours and were paid $10. Then on Sunday, you babysit for another family for 3 hours and were paid $10.50. 

Find the hourly rate that you were paid on each day. Which family do you want to work for again? (That is which one paid your more per hour?)

We used a table to organize the information

Day	Total	Time	Rate
Saturday	$10	2  ½ hours	$__/hour
Sunday	$10.50	3 hours	$__/hour

Saturday:  Amount paid/time = 10/2.5 = $ 4/hour

Sunday: Amount paid/ time = 10/3 = $3.50/hour

Your hourly rate was greater on Saturday.

Two rates for answering questions on a test are given below. 
We wrote each as a unit rate

60 minutes/ 75 questions  and   75 questions/ 60 minutes

for  60 minutes/ 75 questions  we found it was 0.8 min/question

and

for  75 questions/ 60 minutes , we found it was 1.25 questions/ min

Both rates are equivalent and would allow you to complete the test on time. However, it would be easier to use the rate of 0.8 min/question to figure out how long it took you per question!

You drive 1350 miles in 3 days Each day you drive for 9 hours. What is your speed in miles per hour?  

First you need to calculate how many hours you drove. 3(9)= 27à so you drove 27 hours

1350miles/27 hours = 50miles/hour