Problem 10 · 2025 Math Kangaroo
Medium
Ratios, Rates & Proportions
ratioproportion
Max draws a large circle in the sand and Lisa adds the letters A, B, C and D. Starting together from point A, Lisa runs clockwise and Max runs anti-clockwise around the circle (see picture). They meet for the first time at B, then at C, then at D, and then again at A. How many times has Max run around the circle by then?
Show answer
Answer: C — 3 times
Show hints
Hint 1 of 2
Each time they meet, together they have covered one more full circle.
Still stuck? Show hint 2 →
Hint 2 of 2
Find what fraction of the circle Max covers before the first meeting, then scale up to the total laps.
Show solution
Approach: use the constant speed ratio across the meetings
- Going opposite ways, between meetings the two together cover one whole circle.
- They first meet at B after Max has gone three quarters of the way around (A to D to C to B), so Max is 3 times faster.
- From the start until they meet again at A, together they cover 4 circles.
- Max therefore covers 3 of those 4 circles, so Max ran around 3 times - option C.
Mark:
· log in to save