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 ?
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 ?
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 ?
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 ?
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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