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Question

# A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

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Solution

## We know that Speed = Distance / Time. This means Time = Distance / Speed Let "u" be speed upstream and "d" be speed downstream Using this we get: 30/u + 28/d = 7 ------------- (i) We are also given that the boat can travel up and down in 5 hours. This means: 21/u + 21/d = 5 ------------- (ii) Multiplying (ii) by 30/21, we get 30/u + 30/d = 50/7 --------- (iii) Subtracting (iii) from (i), we get: d = 14 km/hr Inputting this in equation (i), we get u = 6 km/hr We know that Speed Upstream = Speed of boat - Speed of stream and Speed Downstream = Speed of boat + Speed of stream From here we get two more equations: u = Sb - Sr, this means: 6 = Sb - Sr ----------- (iv) and d = Sb+Sr, this means: 14 = Sb + Sr ------------- (v) Adding (iv) and (v), we get: Sb = 10 km/hr; substituting this value in equation (iv) we get Sr = 4 km/hr Please note, Sb = Speed of boat in still water and Sr = speed of stream.

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