GK 2018 Q20
20. Ruth and Sarah decide to have a race. Ruth runs around the perimeter of the pool shown in the diagram while Sarah swims lengths of the pool.
Ruth runs three times as fast as Sarah swims. Sarah swims six lengths of the pool in the same time Ruth runs around the pool five times.
How wide is the pool?
- A 25 m
- B 40 m
- C 50 m
- D 80 m
- E 180 m
Grey Kangaroo 2018, Question 20. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 40 m
Let the width of the pool be \(x\) m. Therefore the total distance Ruth runs is \(5(2 \times 50 + 2x)\) m = \((500 + 10x)\) m. The total distance Sarah swims is 6 × 50 m = 300 m. Since Ruth runs three times as fast as Sarah swims, \(500 + 10x = 3 \times 300\). Therefore \(10x = 400\) and hence \(x = 40\).
Solution © UK Mathematics Trust, from the GK 2018 solutions.