# 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. 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. 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