Natalie of West Flegg Middle School sent in the solution which we have reproduced below and Rachel from Flegg High School also sent a good solution to this one. Thank you both!
This is Natalie's solution:
First I drew a circle and worked out how long it would take Anne to get a quarter of the way around, and an eighth of the way around.
I divided 40 by 4 (10) and then 10 by 2. Then I worked out where Anne would be after 15 seconds.
After working this out I divided 15 by 5 (3). Now I knew how long Brenda would take to get an eighth of the way around, so I timesed 3 by 8 (24). Brenda takes 24 seconds to get round the track!
After thinking this out I divided 60 (amount of seconds) by 5 (amount of half laps Cathy will have to do to catch Anne up). The answer came to 12. To find out Cathy's full lap time, I timesed this by 2 (24). Cathy and Brenda take the same amount of time to get around the track. They meet every 12 seconds.
Natalie drew some more circuit diagrams to check this. Well done Natalie.