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Question

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 kmph, find the speed of the boat in still water.

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Solution

Let the speed of the boat in still water be x km/hr.It is given that the speed of the stream is 2 km/hr. Speed upstream = (x 2) km/hr Speed downstream = (x + 2) km/hrTime taken to go 8 km downstream = 8(x + 2) hrTime taken to go 8 km upstream = 8(x 2) hr 8(x + 2) + 8(x 2) = 14060 8(x + 2) + 8(x 2) = 10060 8(x 2) + 8(x + 2)(x 2)(x + 2) = 53 16xx2 4 = 53 3 × 16x = 5(x2 4) 48x = 5x2 20 5x2 48x 20 = 0 5x2 (50 2)x 20 = 0 5x2 50x + 2x 20 = 0 5x(x 10) + 2(x 10) = 0 (x 10)(5x + 2) = 0 x 10 = 0 or 5x + 2 = 0 x = 10 or x = 25 x = 10 ( Speed cannot be a negative fraction) Speed of the boat in still water = 10 km/hr

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