EXPLORING RATES

Commonly used rates like miles per hour make it easy to understand and compare rates.

Example 1 : 

Jeff hikes 1/2 mile every 15 minutes, or 1/4 hour. How far does he hike in 1 hour?  

Solution :

We can use proportion to solve this problem. 

Let 'a' be the number of miles covered by Jeff in 1 hour. 

Then, we have

1/2 : 1/4  =  a : 1

1 x 1/2  =  (1/4)a

1/2  =  a/4

2  =  a

So, Jeff hikes 2 miles in 1 hour.

Examples 2 :

At a summer camp, the campers are divided into groups. Each group has 16 campers and 2 cabins. How many cabins are needed for 112 campers ?

Solution :

First we have to find how many campers can accommodate in one cabin. 

To find the number of campers accommodated in 1 cabin, we have to divide 16 by 2.

16/2  =  8

8 campers can accommodate in 1 cabin. 

To find the number of cabins required for 112 campers, we have to divide 112 by 8.

112/8  =  14

So, 14 cabins needed for 112 campers.

Examples 3 :

If 350 miles of distance covered 7 hours, find the distance covered by 6 hours ?

Solution :

First we have to find how many miles of distance covered in 1 hour.  

To find the distance covered in 1 hour, we have to divide 350 by 7.

350/7  =  50

In 1 hour, 50 miles of distance covered. 

In 6 hours, the distance covered  =  6 x 50  =  300 miles.

Examples 4 :

Petra jogs 3 miles in 27 minutes. Find the unit rate in minutes per mile. How long would it take her to jog 5 miles ?

Solution :

To find the unit rate in minutes per mile, we have to divide 27 minutes by 3 miles.

27 ÷ 3  =  27/3  =  9

Unit rate in minutes per mile  =  9

That is, it takes 9 minutes to cover 1 mile of distance. 

To find the time taken to cover 5 miles, we have to multiply 5 and 9

5 x 9  =  45

Therefore, it will take 45 minutes to cover 5 miles of distance. 

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