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.

  1. 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.
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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.


  8. 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.
  9. 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
  10. 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 = 721000 meters / 3600 seconds

    = (72000/3600) (meters / second) = 20 meters / second

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Updated: 20 January 2017 (A Dendane)