Detailed Solutions to Questions on Finding Unit Rate
Detailed solutions to the questions on finding rate in math.
Find the unit rate in each of the following situations.

I traveled 300 kilometers in 5 hours. Find the unit rate in kilometers / hour
Solution
Unit Rate in traveling 300 kilometers in 5 hours is
300 kilometers/ 5 hours = (300 / 5) (km / hour) = 60 km/hour
Note The above unit rate is also called speed.

An international phone call costs $10 for 4 minutes. Find the unit rate in dollars / minute.
Solution
Unit Rate in cost of $10 for 4 minutes
10 dollars / 4 minutes = (10/4)(dollars/minute) = 2.5 dollars / minute

Joelle reads 18 pages in 9 minutes. Find the unit rate in pages/minute
Solution
Unit Rate in reading 18 pages in 9 minutes
18 pages / 9 minutes = (18/9)(pages/minute) = 2 pages / minute

A car consumes 12 gallons of fuel for a distance of 240 miles. Find the unit rate in miles / gallon.
Solution
Unit Rate in consuming 12 gallons of fuel for a distance of 240 miles
240 miles / 12 gallons = (240/12)(miles/gallon) = 20 miles / gallon

A pump moves 45 liters of water every 5 minutes. What is the unit rate of the pump in liters / minute?
Solution
Unit Rate in pumping 45 liters in 5 minutes
45 liters / 5 minutes = (45/5)(liters/minute) = 9 liters / minute

Joe bought 4 kilograms of apples at the cost of $16. Find the unit rate (or price of 1 kilogram) in dollars / kilogram
Solution
Unit Rate (or cost of one kilogram) of apple
16 dollars / 4 kilograms = (16/4)(dollars/kilogram) = 4 dollars / kilogram

Which moves faster, an object A that moves 15 centimeters every 5 seconds or an object B that moves 24 centimeters every 8 seconds?
Solution
One way to compare the speed of the two object is to find the unit rate of each.
Unit Rate of object A
15 centimeters / 5 second = (15/5)(centimeters / second) = 3 cm / second
Unit Rate of object B
24 centimeters / 8 second = (24/8)(centimeters / second) = 3 cm / second
Both objects are moving at the same rate or speed.

Car A consumes 12 gallons of fuel for a distance of 240 miles. Another car B consumes 25 gallons for a distance of 550 miles. Which of the two cars travels further per gallon?
Solution
Unit Rate of consumption of car A
240 miles / 12 gallons = (240/12)(miles/gallon) = 20 miles / gallon
Unit Rate of consumption of car B
550 miles / 25 gallons = (550/25) (miles / gallon) = 22 miles / gallon
Car B travels further per gallon.

Convert the unit rate 60 kilometers/hour into kilometers / minute.
Solution
Convert 1 hour into minutes using: 1 hour = 60 minutes. Hence
60 kilometer/hour = 60 kilometer/60 minutes = (60/60) (km/minute) = 1 km / minute

Convert the unit rate 72 kilometers / hour into meters / second.
Solution
Convert kilometers into meters using 1 kilometer = 1000 meters and 1 hour into seconds using 1 hour = 3600 seconds. Hence
72 kilometer/hour = 72×1000 meters / 3600 seconds
= (72000/3600) (meters / second) = 20 meters / second


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Updated: 20 January 2017 (A Dendane)