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    Question

    A boat covers the distance between two points downstream

    in 2 hours and upstream in 3 hours. If the speed of the stream is 3 km/h, find the speed of the boat in still water and the distance between the two points.
    A 22 km Correct Answer Incorrect Answer
    B 28 km Correct Answer Incorrect Answer
    C 36 km Correct Answer Incorrect Answer
    D 32 km Correct Answer Incorrect Answer

    Solution

    Let speed of boat in still water = u km/h Speed of stream = v = 3 km/h Downstream speed = u + v, upstream speed = u − v Let distance = d km. Downstream: d/(u + v) = 2 …(1) Upstream: d/(u − v) = 3 …(2) From (1): d = 2(u + v) From (2): d = 3(u − v) Equate: 2(u + v) = 3(u − v) 2u + 2v = 3u − 3v ⇒ u = 5v = 5 × 3 = 15 km/h Then d = 2(u + v) = 2(15 + 3) = 36 km Answer: Boat speed = 15 km/h, distance = 36 km.

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