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

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) = 3cups

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

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

= 8 cups

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 miles

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

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

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 miles

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 gallons

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

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