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
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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