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Find Speed, Distance and Time

In this worksheet, students will use the Distance, Speed, Time formulae pyramid to identify which formula to use to find the answer in questions involving these three metrics.

'Find Speed, Distance and Time' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

A very common question type to see on GCSE exams are problems involving compound units related to speed, distance and time.

The most challenging element when completing questions about speed, distance and time is remembering the relevant formulae.

 

 

How to Remember the Formulae 

The easiest approach is to memorise the formulae triangle shown below, which we can then use to find the any single formula:

 

 

 

 

How To Use This Diagram

Simple, just highlight the element you are trying to find (we've done it with a red circle) and the formula to find this will use what's left:

 

 

 

Let's look at these formulae in action now.

 

 

e.g. A car travels at 40 mph for 3 hours. How far does it go?

 

The first step in these calculations is always to decide what we are trying to find.

For this one, we are asked "How far...?" so this must be a distance question:

D = S × T

 

Now we can simply plug our numbers into this formula:

D = 40 × 3 = 120

 

The last question that we need to ask ourselves is what the measurement units should be.

The trick here is that they are always the same as one of the other units.

The speed here is given in miles per hour, so the distance must be in miles.

 

So Distance = 120 miles

 

 

 

Let's try one more example to check we have these formulae clear in our mind.

 

 

e.g. A bike travels 100 m in 5 seconds. What is its average speed?

 

Once again, we need to decide which formula.

Don't worry that the question asks for average speed, we can still use the same formulae:

S = D ÷ T

 

Plugging in our numbers gives us:

S = 100 ÷ 5 = 20

 

Our original units were metres per second (remember, the units are in the question).

 

So Speed = 20 m/s

 

 

 

In this activity, we will use the Distance, Speed, Time formulae pyramid to identify which formula to use to find the answer to questions involving these three metrics using the methods shown above. 

Type two words into the spaces to complete the sentence below. 

A car travels 80 miles in 2 hours.

 

What is its average speed?

40 mph

160 mph

100 mph

Find the average speed of a car that travels 280 miles in 4 hours.

 

Just type a number as your answer without any units, as these have already been provided for you. 

40 mph

160 mph

100 mph

Type two words into the spaces to complete the sentence below. 

40 mph

160 mph

100 mph

A car travels 50 km/h in 4 hours.

 

How far has the car travelled? 

54 km

12.5 km

200 km

How far does a cyclist travel if they ride at 25 m/s for 28 seconds?

 

Just type a number as your answer without any units, as these have already been provided for you. 

54 km

12.5 km

200 km

Type two words into the spaces to complete the sentence below. 

54 km

12.5 km

200 km

A train travels 70 miles at 10 mph

 

How long does this journey take? 

80 hrs

7 hrs

700 hrs

How long will a jogger take to run 40 miles at a speed of 8 miles per hour?

 

Just type a number as your answer without any units, as these have already been provided for you. 

80 hrs

7 hrs

700 hrs

Match each distance and speed on the left with the correct time taken for each journey on the right.

Column A

Column B

50 miles, 25 mph
2 hours
10 km, 4 hours
16 seconds
400 m, 25 m/s
2 hrs 30 minutes
9 miles, 2 mph
4.5 hours
  • Question 1

Type two words into the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Just remember, we need to use the formulae triangle and look at what's left, when we cover the metric we are searching for. If we cover up Speed in the triangle, we are left with: Distance ÷ Time As with any division sum, it is important to get these two metrics the right way round or we will not reach the correct answer.
  • Question 2

A car travels 80 miles in 2 hours.

 

What is its average speed?

CORRECT ANSWER
40 mph
EDDIE SAYS
It's all about identifying the correct formula to use. We are looking for the Speed here, so if we cover this up in our triangle, we are left with: Speed = Distance ÷ Time Now, let's substitute our numbers into this formula: Speed = 80 ÷ 2 Speed = 40 mph
  • Question 3

Find the average speed of a car that travels 280 miles in 4 hours.

 

Just type a number as your answer without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We need to use the same formula again here. Speed = Distance ÷ Time Speed = 280 ÷ 4 Speed = 70 mph
  • Question 4

Type two words into the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Just remember, we need to use the formulae triangle and look at what's left, when we cover the metric we are searching for. If we cover up Distance in the triangle, we are left with: Distance = Speed × Time As with any multiplication sum, we can choose to calculate these numbers either way round, so 'Speed × Time' or 'Time × Speed' will both give us the same answer.
  • Question 5

A car travels 50 km/h in 4 hours.

 

How far has the car travelled? 

CORRECT ANSWER
200 km
EDDIE SAYS
The use of the word 'How far...?' in the question allows us to know that we are looking for a Distance here. If we are looking for the Distance here and cover this up in our triangle, we are left with: Distance = Speed × Time Now, let's substitute our numbers into this formula: Distance = 50 × 4 Distance = 200 km
  • Question 6

How far does a cyclist travel if they ride at 25 m/s for 28 seconds?

 

Just type a number as your answer without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Again we are looking for a Distance here, so we need to use again: Distance = Speed × Time Now, let's substitute our numbers into this formula: Distance = 24 × 28 Distance = 700 m
  • Question 7

Type two words into the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Just remember, we need to use the formulae triangle and look at what's left, when we cover the metric we are searching for. If we cover up Time in the triangle, we are left with: Time = Distance ÷ Speed As with any division sum, it is important to get these two metrics the right way round or we will not reach the correct answer.
  • Question 8

A train travels 70 miles at 10 mph

 

How long does this journey take? 

CORRECT ANSWER
7 hrs
EDDIE SAYS
It's all about identifying the correct formula to use here. We are looking for the Time here, so if we cover this up in our triangle, we are left with: Time = Distance ÷ Speed Now, let's substitute our numbers into this formula: Time = 70 ÷ 10 Time = 7 hours
  • Question 9

How long will a jogger take to run 40 miles at a speed of 8 miles per hour?

 

Just type a number as your answer without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Again we are looking Time here so we need to use: Time = Distance ÷ Speed Now, let's substitute our numbers into this formula: Time = 40 ÷ 8 Time = 5 mph
  • Question 10

Match each distance and speed on the left with the correct time taken for each journey on the right.

CORRECT ANSWER

Column A

Column B

50 miles, 25 mph
2 hours
10 km, 4 hours
2 hrs 30 minutes
400 m, 25 m/s
16 seconds
9 miles, 2 mph
4.5 hours
EDDIE SAYS
The tricky ones to calculate here are those that don't use whole numbers. So if we reach an answer of 4.5 hours, the 4 represents 4 hours but, don't forget, that 0.5 hours means 30 minutes, not 50! Let's work through each calculation one at a time to find the matches. For each, we are looking for 'Time' so we need to use the formula: Time = Distance ÷ Speed Time (1) = 50 ÷ 25 = 2 hours Time (2) = 10 ÷ 4 = 2. 5 hours = 2 hours 30 minutes Time (3) = 400 ÷ 25 = 16 seconds Time (4) = 9 ÷ 2 = 4.5 hours You can also use the units to help you in questions like this, as only one option uses the measurement 'm/s' which must match with 'seconds'. You can now use the Distance, Speed, Time formula pyramid to create and solve expressions to find one of these missing metrics.
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