Question
A man can row a boat in still water at a speed of 8
km/h. He rows downstream for 1 hour and then returns upstream. If the total time taken for the entire journey is 2.5 hours, find the speed of the stream.Solution
Let the speed of the stream be x km/h. Downstream speed: Speed of boat + speed of stream = 8 + x km/h Upstream speed: Speed of boat - speed of stream = 8 - x km/h Distance downstream: Since the man rows downstream for 1 hour, the distance downstream (d) is: d = Speed × Time = (8 + x) × 1 = 8 + x km Time taken upstream: Time = Distance / Speed = (8 + x) / (8 - x) hours According to the problem, the total time for the journey is 2.5 hours: Time downstream + Time upstream = 2.5 => 1 + (8 + x) / (8 - x) = 2.5 Subtracting 1 from both sides: (8 + x) / (8 - x) = 1.5 Now, cross-multiplying: 8 + x = 1.5(8 - x) 8 + x = 12 - 1.5x x + 1.5x = 12 - 8 2.5x = 4 x = 4 / 2.5 x = 1.6 km/h Correct Answer: a) 1.6 km/h.
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