Multiple choice

A stream runs at 1 km/hr. A motor boat goes 35 km upstream and returns to the starting point in 12 hours. The speed of the motor-boat in still water (in km/hr) is

  1. 6

  2. 7

  3. 8

  4. 8.5
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A Correct answer
Explanation

Let speed in still water be x. Upstream speed = x-1, downstream = x+1. 35/(x-1) + 35/(x+1) = 12. 35(x+1 + x-1) = 12(x^2 - 1). 70x = 12x^2 - 12. 6x^2 - 35x - 6 = 0. (6x+1)(x-6) = 0. x = 6.

AI explanation

Let the speed of the motor-boat in still water be x km/hr, making the downstream speed (x + 1) and the upstream speed (x - 1). Using the total time of 12 hours for the 35 km round trip, we set up the equation 35 / (x + 1) + 35 / (x - 1) = 12. Multiplying by (x^2 - 1) gives 35(x - 1) + 35(x + 1) = 12(x^2 - 1), which simplifies to 70x = 12x^2 - 12, or 6x^2 - 35x - 6 = 0. Factoring this quadratic equation yields (6x + 1)(x - 6) = 0, meaning the positive speed is 6 km/hr.

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