14.4 Distance, Speed and Time

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: speed calculations, average speed, distance–time graphs and speed–time graphs. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Use speed = distance ÷ time and rearrange it to find distance or time
• Change between hours and minutes in speed questions and work out average speed for a journey
• Draw and interpret distance–time graphs
• Interpret speed–time graphs, including acceleration and the distance travelled

Key words

• Average speed: Total distance ÷ total time for the whole journey.
• Distance–time graph: A graph of how far something is from a starting point as time passes. The gradient is the speed.
• Speed–time graph: A graph of speed against time. The gradient is the acceleration.
• Acceleration: How quickly speed changes, in m/s². A negative value is a deceleration.

Speed, distance and time

Key fact: speed = distance ÷ time distance = speed × time time = distance ÷ speed

Time must be in the same units as the speed. In km/h, time must be in hours. Change minutes to hours by dividing by 60.

• Hours; 15 0.25; 20 1/3; 30 0.5; 45 0.75; 6 0.1; 12 0.2; 36 0.6

Worked example: distance and time

(a) A train travels for 2 hours 15 minutes at 96 km/h. 2 h 15 min = 2.25 h. Distance = 96 × 2.25 = 216 km.
(b) Ana runs 10 km at 12 km/h. Time = 10 ÷ 12 = 0.8333… h. 0.8333… × 60 = 50 minutes.

Answer: 216 km; 50 minutes

Average speed

For a journey in stages, add up the distances and the times. Do not take the mean of the two speeds.

Worked example: two stages

A delivery driver travels 30 km at 60 km/h, then 50 km at 100 km/h.
Times: 30 ÷ 60 = 0.5 h and 50 ÷ 100 = 0.5 h. Total = 1 h.
Average speed = 80 km ÷ 1 h = 80 km/h.

Answer: 80 km/h

Distance–time graphs

• A sloping line means moving. The steeper the line, the faster the speed.
• A horizontal line means stopped (the distance is not changing).
• A line sloping down means coming back towards the start.

Worked example: reading the graph

A: 30 km in 1 hour, so speed = 30 km/h. B: stopped for 0.5 hours (30 minutes).
C: 30 km in 1.5 hours, so speed = 30 ÷ 1.5 = 20 km/h.

Answer: 30 km/h, 30 minutes, 20 km/h

Speed–time graphs

On a speed–time graph a horizontal line means a constant speed (not stopped!). A line going up is acceleration; a line going down is deceleration.

Key fact: Acceleration = gradient = change in speed ÷ time. Distance travelled = area under the graph.

Worked example: using the speed–time graph

Acceleration in the first 5 s = 10 ÷ 5 = 2 m/s².
Distance = triangle + rectangle + triangle = ½ × 5 × 10 + 10 × 10 + ½ × 4 × 10 = 25 + 100 + 20 = 145 m.

Answer: 2 m/s²; 145 m

Common mistakes

• Using minutes in a km/h calculation. 20 minutes is 1/3 hour, not 0.2 hours.
• Writing 2.25 hours as 2 hours 25 minutes. It is 2 hours 15 minutes.
• Finding average speed by averaging the speeds.
• Reading a horizontal line on a speed–time graph as “stopped”. It means a steady speed.

Revision questions

Try these, then check your answers below each one.

Question 1. A van travels for 2.5 hours at 64 km/h. How far does it travel?

Answer: 160 km

Working: 64 × 2.5 = 160 km.

Question 2. Write 2 hours 24 minutes in hours, as a decimal.

Answer: 2.4 hours

Working: 24 ÷ 60 = 0.4, so 2.4 hours.

Question 3. How many minutes does it take to cycle 45 km at 18 km/h?

Answer: 150 minutes

Working: 45 ÷ 18 = 2.5 hours = 150 minutes.

Related lessons

• Previous lesson: 14.3 Compound Measures
• Next lesson: 14.5 Direct and Inverse Proportion
• In this chapter: 14.1 Percentages
• In this chapter: 14.2 Growth and Decay

Continue in the full course

This lesson is section 14.4 (EGCMF1404) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.