Problem 24 · 2018 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-timeratio
Simon runs along the edge round a 50 m long rectangular swimming pool, while at the same time Jan swims lengths in the pool. Simon runs three times as fast as Jan swims. While Jan swims 6 lengths, Simon manages 5 rounds around the pool. How wide is the swimming pool?
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Answer: B — 40 m
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Hint 1 of 2
In the same time, compare how far each travels using the 3-to-1 speed ratio.
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Hint 2 of 2
Find the pool's perimeter, then solve for the unknown width from 2(length + width).
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Approach: equal time, speed ratio gives the perimeter
- Jan swims 6 lengths = 6 · 50 = 300 m; in the same time Simon (3 times as fast) covers 900 m in 5 rounds.
- So one round (the perimeter) is 900 : 5 = 180 m.
- Then 2 · (50 + width) = 180 gives width = 40 m.
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