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A boat travels 30 km downstream and 18 km upstream in 4 hours. It also travels 40 km downstream and 24 km upstream in 5 hours 20 min. Find the speed of the boat and the stream.
ABoat 8, Stream 1
BBoat 10, Stream 2
CBoat 15, Stream 5
DBoat 12, Stream 3
Answer & Solution
Correct answer: D. Boat 12, Stream 3
Let b = boat speed, s = stream speed. Downstream b + s, upstream b − s. Solve 30/(b+s) + 18/(b−s) = 4 and 40/(b+s) + 24/(b−s) = 16/3. Substitute u = 1/(b+s), v = 1/(b−s): system gives u = 1/15, v = 1/9. So b + s = 15, b − s = 9 ⇒ b = 12, s = 3.
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