CONVERT UNIT RATES WORD PROBLEMS 

Convert Unit Rates Word Problems :

In this section, we will learn, how to solve word problems by converting the given rate into unit rate. 

First let us understand what is unit rate. 

Definition of Unit Rate : 

Unit rate compares the given amount to one unit of another measure

(or)

The ratio between the given value and 1 

(or)

Comparing the given amount or value to 1

Examples :

1. If 8 dolls are made in 4 days, 

then number of dolls made in 1 day  =  2

2. If David earns $180 in 9 hours, 

then number of dollars earned by him in 1 hour  =  $ 20

3. If there are 16 cups in 4 quarts,

then the number of cups in 1 quart = 4 

Liquid Measurements - Unit Rates

From the above picture, we can get the following unit rates related liquid measurements.

1 gallon  =  16 cups

1 gallon  =  8 pints

1 gallon  = 4 quarts 

1 quart  =  2 pints

1 quart  =  4 cups 

1 pint  =  2 cups 

Convert Unit Rates Word Problems

Problem 1 :

In a business, if A can earn $7500 in 2.5 years, find the unit rate of his earning per month. 

Solution : 

Given : Earning in 2.5 years  =  $7500

1 year  =  12 months 

2.5 years  =  2.5 ⋅ 12  =  30 months   

Then, earning in 30 months  =  $7500

Therefore, earning in 1 month  =  7500 / 30  =  $250

Hence, the unit rate of his earning per month is $250.

Problem 2 :

If David can prepare 2 gallons of juice in 4 days, how many  cups of juice can he prepare per day ? 

Solution : 

No of gallons of juice prepared in 4 days  =  2 gallons

1 gallon  =  16 cups

So, no. of cups of juice prepared in 4 days  =  2 ⋅ 16  =  32 cups

Therefore, David can prepare 32 cups of juice in 4 days. 

Then, no. of cups of juice prepared in 1 day  =  32 / 4  =  8

Hence, David can prepare 8 cups of juice in 1 day. 

Problem 3 :

If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute.  

Solution : 

No of miles covered in 3 hours  =  360 

Then, no. of miles covered in 1 hour  =  360 / 3  =  120 

1 hour  =  60 minutes

So, no. of miles covered in 60 minutes  =  120

Then, no. of miles covered 1 minute  =  120 / 60  =  2

Hence, John can cover 2 miles in 1 minute. 

Problem 4 : 

75 basketballs cost $1,143.75. Find the unit rate in price per basketball. 

Solution :

Given : 75 basketballs cost $1,143.75

Then, price of one basket ball  =  1143.75 / 75  =  15.25

Hence, the unit rate in price per basket ball is $ 15.25

Problem 5 :

In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How was his unit rate in price per week ? 

Solution :

Given : Miguel raised $2, 372.50 in 36.5 weeks 

Then, amount raised in one week  =  2372.5 / 36.5  =  65

Hence, the unit rate in price per week was $65.

Problem 6 :

A person can cover a distance of 84 miles in 4 gallons of fuel. If he has 2.5 gallons, how many miles can he cover ?

Solution : 

Given : 84 miles can be traveled in 4 gallons. 

Then, no. of miles traveled in 1 gallon  =  84 / 4  =  21

Therefore, no. of miles traveled in 2.5 gallons  is

=  21 ⋅ 2.5  

=  52.5   

Hence, 52.5 miles traveled in 2.5 gallons of fuel. 

Problem 7 :

If a person drinks 8 cups of apple juice per month, how many gallons will he drink in one year?

Solution : 

Given : 8 cups in one month 

1 year  =  12 months 

So, no. of cups in 1 year  =  8 ⋅ 12  =  96 cups

1 gallon  =  16 cups

Therefore, no. of gallons in 1 year  =  96 / 16  =  6 

Hence, he will drink 6 gallons of apple juice in 1 year.

Problem 8 :

My David earns $416 in 8 hours. How much does earn in 2.8 hours ?

Solution : 

Given : Earning in 8 hours  =  $ 416

Earning in 1 hour  =  $ 52

Earning in 2.8 hours  =  52 ⋅ 2.8  =  145.6

Hence, Mr. David will earn $145.6 in 2.8 hours.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems using unit rates.

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