Multiple choice

The water in a river flows at a rate of 1 km/hr. A boat goes 35 km upstream and returns to the starting point in 12 hours. The speed of the 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 boat speed be v. Upstream speed is v - 1, downstream is v + 1. Time = 35/(v-1) + 35/(v+1) = 12. 35(v+1 + v-1) / (v^2 - 1) = 12. 70v = 12v^2 - 12. 12v^2 - 70v - 12 = 0. 6v^2 - 35v - 6 = 0. (6v + 1)(v - 6) = 0. v = 6.

AI explanation

Let the speed of the boat in still water be b km/hr; the downstream speed is (b plus 1) and the upstream speed is (b minus 1). The total time taken for the 35 km upstream and 35 km downstream journey is 12 hours, giving the equation 35 divided by (b minus 1) plus 35 divided by (b plus 1) equals 12. Multiplying by the common denominator yields 35 times (b plus 1) plus 35 times (b minus 1) equals 12 times (b squared minus 1), which simplifies to 70b equals 12b squared minus 12. Rearranging this gives the quadratic equation 6b squared minus 35b minus 6 equals 0, which factors to (6b plus 1) times (b minus 6) equals 0. Discarding the negative value leaves b equal to 6 km/hr.

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