Speed, Distance and Time

In the exam you are given two of speed, distance and time, and asked to work out the third. Short questions, such as finding an average speed from a distance and a time, are worth 2 marks.

Questions worth 3 or 4 marks give a time in hours and minutes, ask for a time of arrival, change a speed from km/h into m/s, or describe a journey in two parts. Most of the marks lost are for working with time, not for the speed formula.

Speeds are given in kilometres per hour (km/h), miles per hour (mph) or metres per second (m/s). Distance-time graphs have their own page.

Speed is how far something travels in each unit of time. A speed of 60 km/h means 60 kilometres in each hour.

A car speeds up and slows down on a journey. Its average speed is the steady speed that would cover the same distance in the same time.

To find a speed, divide the distance by the time:

\text{speed}=\frac{\text{distance}}{\text{time}}

Kilometres and hours give km/h. Miles and hours give mph. Metres and seconds give m/s.

At 40 km/h for 3 hours you travel 40 km three times, so the distance is 40\times3=120 km. The same fact gives two more formulae:

\text{distance}=\text{speed}\times\text{time}

\text{time}=\frac{\text{distance}}{\text{speed}}

Cover the one you want to find. Covering D leaves S and T side by side, so multiply. Covering S leaves D over T, so divide distance by time. Covering T leaves D over S, so divide distance by speed.

Then ask whether your answer makes sense. People walk at about 5 km/h, so a walking speed of 500 km/h means you multiplied when you should have divided.

There are 60 minutes in an hour, not 100. So 2 hours 15 minutes is not 2.15 hours.

To change minutes into hours, divide by 60. For example, 45 minutes is 45\div60=0.75 hours, so 3 hours 45 minutes is 3.75 hours.

To change a decimal of an hour into minutes, multiply the decimal part by 60. For example, 2.6 hours is 2 hours and 0.6\times60=36 minutes. It is not 2 hours 6 minutes.

You can also work in minutes. A speed in kilometres per minute becomes km/h when you multiply it by 60, because there are 60 minutes in an hour.

For a speed in m/s, the distance must be in metres and the time in seconds. There are 1000 metres in a kilometre and 60 seconds in a minute.

For example, a runner covers 1.2 km in 5 minutes. That is 1200 metres in 300 seconds, so the speed is 1200\div300=4 m/s. Working out 1.2\div5 instead gives kilometres per minute, not m/s.

To change a speed from km/h into m/s, change the kilometres into metres and the hour into seconds. One hour is 60\times60=3600 seconds. So 36 km/h is 36000 metres in 3600 seconds, which is 10 m/s.

For a journey in parts, add up all the distances and add up all the times. Then divide:

\text{average speed}=\frac{\text{total distance}}{\text{total time}}

A stop counts in the total time, even though no distance is travelled.

Do not find the mean of the two speeds. That only works when both parts take the same time, and they usually do not.

Some questions give a time limit for a whole journey and ask what speed is needed for the rest of it. Work out the time left and the distance left. Then divide the distance left by the time left.

For example, a driver has 3 hours for a 210 km journey. The first 90 km at 60 km/h take 90\div60=1.5 hours. That leaves 3-1.5=1.5 hours for the other 210-90=120 km. So the speed needed is 120\div1.5=80 km/h.

• Multiplying when you should divide. Speed is distance divided by time, and time is distance divided by speed; only distance is found by multiplying.
• Writing minutes as a decimal of an hour. Divide the minutes by 60, not 100: 1 hour 45 minutes is 1.75 hours, not 1.45
• Reading a decimal of an hour as minutes. Multiply the decimal part by 60: 1.25 hours is 1 hour 15 minutes, not 1 hour 25 minutes.
• Finding the mean of the speeds. For a whole journey, divide the total distance by the total time.
• Mixing units. For m/s, change kilometres into metres by multiplying by 1000, and hours or minutes into seconds.
• Giving the journey time when asked when it arrives. Add the journey time to the starting time.