Speed, Distance, Time
Speed, Distance, Time Calculations
Your child may be asked to work out the speed, distance or time. This could be in the context of a journey to school or something similar. They will usually be given two of the quantities and have to work out the third quantity.
Formulae
Speed, distance and time are quantities that are connected by the following formula.
Speed = Distance \div Time
This version of the formula is helpful when working out the speed but the formula can be rearranged to work out the distance.
Distance = Speed \times Time
Then to work out the time, the formula will be:
Time = Distance \div Speed
Example 1: Finding Time
Example: Timothy walks to school which is 2.5 kilometres away from his house.
He walks at an average speed of 5 kilometres per hour.
How many minutes does it take Timothy to walk to school?
The version of the formula that is most useful for us in this question is:
Time = Distance \div Speed
The distance is 2.5 kilometres and the speed is 5 kilometres per hour.
Your child then needs to be able to substitute these values into the formula.
Time = 2.5 \div 5 = 0.5 hours
The question wants our answer in minutes.
There are 60 minutes in an hour.
0.5 \times 60 = 30 minutes
So, it will take Timothy 30 minutes to walk to school.
Example 2: Finding Distance
Example: Simraj takes the bus to visit her friend’s house.
The bus takes 2 hours and 45 minutes to get to her friend’s house and travels at an average speed of 20 miles per hour.
First, your child needs to convert the time into hours as a decimal.
45 minutes is \dfrac{3}{4} of an hour or 0.75 of an hour.
So, the time becomes 2.75 hours.
Next, your child can choose the appropriate formula to use.
Distance = Speed \times Time
The speed is 20 miles per hour and the time is 2.75 hours.
Substitute the values into the correct version of the formula.
Distance =20 \times 2.75 = 55 miles
So, the distance between Simraj’s house and Simraj’s friend’s house is 55 miles.
Example 3: Finding Speed
Example: Sian has taken her dog for a walk in the park.
She times how long it takes for her dog to run 800 metres.
It takes her dog 3 minutes to run that distance.
Work out the average speed of Sian’s dog.
Give your answer in kilometres per hour.
As the question wants our answer in kilometres per hour, we need to convert the distance to kilometres and the time to hours.
There are 1000 metres in 1 kilometre.
800 \div 1000 = 0.8 kilometres
There are 60 minutes in 1 hour.
3 \div 60 = 0.05 hours
Now that the values are in the correct form we can calculate the average speed using the formula:
Speed = Distance \div Time
Speed = 0.8 \div 0.05 = 16 kilometres per hour
So, the average speed of Sian’s dog is 16 kilometres per hour.
Speed, Distance, Time Example Questions
Question 1: Fergus travels from Sudsworth to Dartwistle to visit his friend.
a) What is the total distance between Sudsworth and Dartwistle?
b) If Fergus travels at an average speed of 36 kilometres per hour, how long will it take for him to get from Sudsworth to Dartwistle?
[3 marks]
a) To find the total distance between Sudsworth and Dartwistle, your child needs to simply add up the distance between Sudsworth and Endthorpe and the distance between Endthorpe and Dartwistle.
The distance between Sudsworth and Endthorpe is 6.1 kilometres.
The distance between Endthorpe and Dartwistle is 4.7 kilometres.
Total distance =4.7 + 6.1 = 10.8 kilometres.
b) Total distance is 10.8 kilometres
Average speed is 36 kilometres per hour.
Your child must choose the correct version of the formula.
Time = Distance \div Speed
Substitute the values in.
Time = 10.8 \div 36 = 0.3 hours
We can convert 0.3 hours into minutes.
0.3 \times 60 = 18 minutes
So, it will take Fergus 18 minutes to get from Sudsworth to Dartwistle.
Question 2: A motorbike is travelling at 50 miles per hour.
How far will it travel in 1 hour and 45 minutes?
[2 marks]
First, your child should recognise that the time needs to be converted into hours as a decimal.
45 minutes = 0.75 hours
So, 1 hour and 45 minutes =1.75 hours.
Now, we can find the total distance the motorbike travelled.
Distance = Speed \times Time
Substitute in our converted values.
Distance = 50 \times 1.75 = 87.5 miles
So, the total distance the motorbike travelled is 87.5 miles.
Question 3: A train travels at a constant speed.
It travels 100 kilometres in 50 minutes.
What distance does it travel when moving for 35 minutes?
[2 marks]
This question uses techniques introduced in the proportion topic.
If the train travels 120 kilometres in 50 minutes then we can work out how many kilometres it travels in 5 minutes.
In 5 minutes:
120 \div 10 = 12 kilometres in 5 minutes.
Now, we can work out how far the train will travel in 35 minutes.
We know that to get from 5 minutes to 35 minutes we multiply by 7, so we need to multiply the distance by 7 to get the distance travelled in 35 minutes.
12 \times 7 = 84 kilometres
So, the train can travel 84 kilometres in 35 minutes.