Question
A boat travels 42 km against the current and 72 km with
the current in a total time of 8 hours. Additionally, it covers a distance of 56 km in still water in 4 hours. Given that the speed of the current exceeds 1.75 km/h, by what percentage is the boat's speed upstream lower than its speed downstream?Solution
Speed of the boat in still water = 56/4 = 14 km/h Let the speed of the stream = x km/h So according to question: 42/(14 – x) + 72/(14 + x) = 8 294 + 21x + 504 –36x = 784 – 4x2 4x2 – 15x + 14 = 0 4x2 – 8x – 7x + 14 = 0 4x(x – 2) – 7(x – 2) = 0 (4x – 7)(x – 2) = 0 x = 2, 7/4 = 2, 1.75 As the speed of the stream is greater than 1.75, the value of x = 2 So the downstream speed and upstream speed of the boat are 16 km/h and 12 km/h respectively. So the desired percentage = (16 – 12)/16 × 100 = 25%
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