Speed, time and distance

Speed, time and distance are three friends who always travel together. If you know any two, you can find the third. This is the secret behind every travel calculation.

What is this?

Distance is how far the trip is. Time is how long the trip takes. Speed is how fast , how much distance per unit time.

The basic rule:

$\text{Distance} = \text{Speed} \times \text{Time}$

If a bus moves at 60 km per hour for 3 hours, it covers 60 × 3 = 180 km.

By rearranging, we get:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

So if we cover 180 km in 3 hours, speed = 180 ÷ 3 = 60 km per hour. And if we need to cover 180 km at 60 km per hour, time = 180 ÷ 60 = 3 hours.

Speed is usually written as km/h (kilometres per hour). A walking speed is around 5 km/h. A cycle: 12 km/h. A scooter: 40 km/h. A car on a highway: 60–80 km/h. A fast train: 100+ km/h.

When speed changes during the trip, we sometimes calculate an average speed by dividing total distance by total time. If a car goes 100 km in 2 hours, the average speed is 50 km/h , even if it sometimes went faster and sometimes slower.

Worked examples

Example 1. A bus moves at 50 km/h. How far in 4 hours?

• Distance = 50 × 4 = 200 km.

Example 2. A train covers 480 km in 6 hours. What is its speed?

• Speed = 480 ÷ 6 = 80 km/h.

Example 3. A scooter moves at 40 km/h. How long to cover 200 km?

• Time = 200 ÷ 40 = 5 hours.

Try it

1. A car runs at 60 km/h for 5 hours. Distance?
2. A cyclist covers 36 km in 3 hours. Speed?
3. A bus runs at 45 km/h. How long for 135 km?
4. A walker moves at 4 km/h. How far in 2 hours?
5. A train covers 300 km in 4 hours. Average speed?

Hands-on

Walking speed. Measure a 50 m distance in your school ground. Walk it at a normal pace and time yourself. Calculate your speed in m per second.

Family trip log. On your next family trip, ask the driver about the distance and the time taken. Compute the average speed yourself. Compare with the speedometer reading.