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

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

**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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