Problem 24 · 2016 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
A motorboat drives in the middle of a stream. Downstream it needs four hours to get from X to Y. In order to drive back from Y to X it needs six hours. Tree trunks are also floating on the stream. How many hours does it take for a tree trunk to float in the middle of the stream from X to Y?
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Answer: E — 24
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Hint 1 of 2
Let the boat speed and current speed combine downstream and oppose upstream.
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Hint 2 of 2
The tree floats at the current's speed alone; find that from the two trip times.
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Approach: relative speeds
- Downstream speed is D/4 and upstream is D/6 (D the distance).
- Subtracting, twice the current is D/4 − D/6 = D/12, so the current is D/24.
- A floating trunk takes D ÷ (D/24) = 24 hours.
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