Maths Week Scotland 2025 - Challenge 4 - The Swifts

Challenge 4 is all about distance, speed and time

Maths teacher Chris Smith and pupils from Grange Academy are here to explain.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

This problem is all about distance, speed and time.

The Swift sisters are training for a 10 km race.

They normally train together but, one morning, Anna Swift is slow to get ready for their training session and Becky Swift starts off on their usual route by herself.

Becky runs at an average speed of 8 km/h, while Anna can run at 9 km/h.

After Becky has been running for 36 minutes, Anna catches up with her.

So can you work out how many minutes after Becky Anna started running?

• You’ll need to know how distance, speed and time are related
• Try concentrating on the sister you know most about first.
• Take care with the units you are using

Worked out the answer? Here's how you can do it.

Step 1

We know Anna catches up after Becky has been running for 36 minutes at 8 kilometres per hour.

First we need to convert minutes into hours.

36 ÷ 60 is 0.6 hours.

Step 2

If we multiply 0.6 hours by her speed of 8 kilometres per hour, we find the distance covered was 4.8km.

0.6 × 8 = 4.8km

Step 3

Anna has run 4.8 km too, so and we can work out how long this took.

4.8 km divided by Anna’s speed of 9 km per hour, multiplied by 60 to give us the time in minutes.

4.8 ÷ 9 x 60 = 32

So Anna ran the 4.8km in 32 minutes.

Step 4

So we now have the time taken for each of them to run the 4.8km at their different speeds we can subtract the time Anna has been running from the time Becky has been running to find the difference

36 - 32 = 4

Anna Swift started 4 minutes after Becky Swift.