# 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

Updated: 20 January 2017 (A Dendane)