Speed, distance and time questions test how quickly an object moves, how far it travels, or how long a journey takes.

What questions occur in this topic?

You may be asked to calculate an unknown speed, distance, or time; compare the speeds of two people or vehicles; find average speed; or solve journeys with stops, changing speeds, or different distances.

Common patterns include trains crossing a pole, platform, or another train; boats moving with or against the stream; races; circular tracks; and objects moving in the same or opposite directions.

The three basic quantities

• Distance: the length of the path travelled.
• Time: the duration taken to travel the distance.
• Speed: the distance travelled per unit of time.

Speed = Distance / Time, Distance = Speed x Time, and Time = Distance / Speed. Keep units consistent before using a formula.

Units and conversions

• 1 kilometre = 1,000 metres; 1 hour = 3,600 seconds.
• 1 m/s = 18/5 km/h.
• 1 km/h = 5/18 m/s.
• Convert minutes to hours for km/h, or to seconds for m/s.

Essential ideas

• Average speed: total distance / total time. For equal distances at speeds a and b, it is 2ab/(a+b).
• Relative speed: add speeds in opposite directions and subtract them in the same direction.
• Changing speed: calculate each part separately, then combine all distances and times.
• Stops: include waiting time unless the question asks only for travelling time.

Special cases

• Trains: crossing a pole uses train length; crossing a platform uses train length + platform length; two trains use the sum of their lengths.
• Boats and streams: downstream speed = still-water speed + stream speed; upstream speed = still-water speed - stream speed.
• Races: compare distances for the same time or times for the same distance.
• Circular tracks: meeting time = distance between objects / relative speed.

How to solve questions

1. Write the known distance, speed, and time values.
2. Convert all values to compatible units.
3. Identify the direction of motion and any stops or stream.
4. Select the correct formula and solve.
5. Check the answer's unit and whether it is reasonable.