CONVERT UNIT RATES WORD PROBLEMS 

In this section, you will learn solving word problems by converting the given rate to 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 

Practice 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

So, 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

So, 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

So, 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

So, 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

So, 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   

So, 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 

So, 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

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

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Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

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Times table shortcuts

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Converting repeating decimals in to fractions

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Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

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