Detailed Solutions to Questions on Finding Unit Rate

The concept of rate in maths and algebra is an important one. Detailed solutions to the questions on finding rate are presented.

Find the unit rate in each of the following situations.

  1. I travelled 300 kilometers in 5 hours. Find the unit rate in kilometers / hour
    Solution
    Unit Rate in travelling 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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