Distance, Speed and Time Problems
Distance, speed and time problems ask pupils to use the relationship between how far something travels, how fast it goes, and how long the journey takes. The three quantities are linked by the formula speed = distance / time, which can be rearranged to give distance = speed x time or time = distance / speed. 11+ papers set these as word problems about journeys, often mixing units (hours and minutes, km and miles) and sometimes asking for an average speed across a journey with more than one stage.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify which of distance, speed and time the question gives, and which one it is asking for.
- Write the correct version of the formula for the missing quantity: distance = speed x time, speed = distance / time, or time = distance / speed.
- Check the units match before calculating: convert minutes to hours (divide by 60) if the speed is given 'per hour', or convert between km and miles if the question mixes units.
- Substitute the known numbers into the formula and calculate carefully, showing your working.
- For an average speed across a journey with more than one stage, find the total distance and the total time separately first, then divide total distance by total time.
- Check the answer's size makes sense for the situation, for example a walking speed of 4 km/h is sensible but 400 km/h is not.
Worked example
A car travels 180 km at an average speed of 45 km/h. How long does the journey take, in hours and minutes?
- Identify that distance = 180 km and speed = 45 km/h are known, and time is required.
- Use time = distance / speed: time = 180 / 45.
- Calculate: 180 / 45 = 4, so the journey takes 4 hours.
- Since 4 is a whole number of hours, there are no extra minutes: the journey takes exactly 4 hours.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A cyclist rides 60 km in 4 hours at a constant speed. Work out her average speed in km/h.Show answer
Answer: 15 km/h (60 / 4 = 15)
Q2A train travels at a constant speed of 80 km/h for 3 hours. How far does it travel?Show answer
Answer: 240 km (80 x 3)
Q3A runner covers 100 m in 20 seconds. Work out his speed in metres per second.Show answer
Answer: 5 m/s (100 / 20)
Q4A coach travels 150 miles at an average speed of 50 mph. How long does the journey take?Show answer
Answer: 3 hours (150 / 50)
Q5A walker covers 9 km in 2 hours 15 minutes. Work out her average speed in km/h.Show answer
Answer: 4 km/h (2 hours 15 minutes = 2.25 hours, 9 / 2.25 = 4)
Q6A plane flies 2,400 km in 4 hours, then a further 600 km in 1 hour. Work out its average speed for the whole journey.Show answer
Answer: 600 km/h (total distance 3,000 km, total time 5 hours, 3,000 / 5 = 600)
Q7True or False: if a car halves its speed but keeps the distance the same, the journey time doubles.Show answer
Answer: True
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A lorry leaves a depot at 09:15 and travels 126 miles at an average speed of 42 mph. At what time does it arrive?
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A cyclist travels the first 20 km of a journey at 16 km/h, then the remaining 12 km at 8 km/h. Work out her average speed for the whole journey, giving your answer to 1 decimal place.
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Free printable worksheet
Want more practice on paper? Download the distance, speed and time problems worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 14 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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