# UNIT RATES

Unit rate is the ratio which describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Some common unit rates are miles per hour, cost per item, earnings per week, etc.

Example 1 :

If 12 chickens lay 36 eggs, how many eggs will be laid by 1 chicken.

Solution :

12 chickens ----> 36 eggs

1 chicken ----> (36/12) eggs

1 chicken ----> 3 eggs

So, one chicken will lay 3 eggs.

Example 2 :

If 192 students can accommodate in 4 buses, how many students can accommodate in  3 buses?

Solution :

To find the number of students accommodated in 3 buses, we have to find the unit rate.

That is, we have to find the number of students can accommodate in 1 bus.

Then, multiply it by 13.

4 buses ----> 192 students

1 bus ----> (192/4) students

1 bus ----> 48 students

3 buses ----> (48 ⋅ 3) students

3 buses ----> 144 students

So, 144 students can accommodate in 3 buses.

Example 3 :

If John can type 2400 words in 1 hour, find the number of words types by him in 13 minutes.

Solution :

To find the number of word typed by John in 13 minutes, we have to find the unit rate.

That is, we have to find the number of words typed by him in 1 minute.

Then, multiply it by 13.

1 hour ----> 2400 words

60 minutes ----> 2400 words

1 minute ----> (2400/60) words

1 minute ----> 40 words

13 minutes ----> (40 ⋅ 13) words

13 minutes ----> 520 words

So, the number of words types by John in 13 minutes is 520 words.

Example 4 :

Cost of one dozen fountain pens is \$180 and cost of 8 ball pens is \$56. Find the ratio of the cost of a fountain pen to the cost of a ball pen.

Solution :

To find the ratio of the cost of a fountain pen to the cost of a ball pen, we have to find the unit rate.

That is, we have to find the cost of each pen.

Cost of 12 fountain pens = \$180.

Cost of one fountain pen = 180/12

Cost of one fountain pen = \$15

Cost of 8 ball pens = \$56.

Cost of one ball pen = 56/8

Cost of one ball pen = \$7

Then, we have

Cost of a fountain pen : Cost of a ball pen = 15 : 7

Example 5 :

David can do 90 units of a work in 180 minutes and Alex can complete 80 units of the same work in 2 hours. Find the ratio of number of units of work completed by David and Alex.

Solution :

To find the ratio of number of units of work completed by David and Alex, we have to find the unit rate.

That is, we have to find the number of units of work completed by each in 1 hour.

David :

180 minutes ----> 90 units

3 hours ----> 90 units

1 hour ----> (90/3) units

1 hour ----> 30 units

Alex :

2 hours ----> 80 units

1 hour ----> (80/2) units

1 hour ----> 40 units

Then, we have

No. of units (David) : No. of units (Alex) = 30 : 40

No. of units (David) : No. of units (Alex) = 3 : 4

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