**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

Hence, 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

Hence, 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 hours, 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.

After having gone through the stuff given above, we hope that the students would have understood "Unit rates".

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