Multiple choice

David has to row his boat 99 km downstream and return the same distance upstream. Speed of the stream is 1 km/hour. If he takes 2 hours less to row the boat downstream than to return upstream, then find the speed of the boat in still water.

  1. 100 km/hour

  2. 80 km/hour

  3. 10 km/hour

  4. 15 km/hour

  5. 20 km/hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed be v. Downstream speed = v + 1. Upstream speed = v - 1. Time difference: 99/(v-1) - 99/(v+1) = 2. 99 * (v+1 - v+1) / (v^2 - 1) = 2. 99 * 2 / (v^2 - 1) = 2. 99 = v^2 - 1. v^2 = 100, v = 10.

AI explanation

Let the speed of the boat in still water be x km/hour. The upstream speed is (x - 1) and the downstream speed is (x + 1). The equation for the time difference is 99/(x - 1) minus 99/(x + 1) equals 2. Solving the equation 99(2) = 2(x^2 - 1) results in 99 = x^2 - 1, so x^2 = 100. Therefore, the speed of the boat in still water is 10 km/hour.

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