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.
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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