A bus leaves at 10:15 and arrives at 12:45 after travelling 140 km. Find its average speed.
- Time taken: 10:15 to 12:45 is 2 hours 30 minutes = 2.5 hours.
- Average speed = total distance ÷ total time = 140 ÷ 2.5.
- 140 ÷ 2.5 = 56.
Answer: 56 km/h
Rates
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A rate tells you how much one quantity changes for each unit of another. Speed is distance per unit of time, density is mass per unit of volume, and a flow rate is volume per unit of time. The word “per” means “divided by”, and the unit shows the formula: km/h is kilometres ÷ hours.
Average speed is the total distance divided by the total time for the whole journey. It is not the average of the separate speeds.
Most errors come from units. Change minutes to hours as a fraction or decimal before using km/h: 20 minutes is 20/60 = 1/3 hour, not 0.2 hour.
Rules to remember
- speed = distance ÷ time; distance = speed × time; time = distance ÷ speed
- average speed = total distance ÷ total time
- density = mass ÷ volume
- population density = number of people ÷ area
- km/h to m/s: divide by 3.6. m/s to km/h: multiply by 3.6.
- minutes to hours: divide by 60, so 45 minutes = 0.75 hour and 2 h 20 min = 2 1/3 h
- A rate per second from a rate per minute: divide by 60.
Common mistake
Writing a time such as 2 hours 30 minutes as 2.3 hours. It is 2.5 hours, because 30 minutes is 30/60 of an hour.
Worked example
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