Multiple choice

A man takes to row 80 km along the stream is half of the time taken to row against the stream. Find the speed of the boat in still water if the speed of stream is 6 km/hr?

  1. 24 km/hr

  2. 20 km/hr

  3. 18 km/hr

  4. 12 km/hr

  5. None of these
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C Correct answer
Explanation

Let v be speed of boat, s = 6. Downstream speed = v+6, upstream = v-6. Time = Distance / Speed. 80/(v+6) = 0.5 * 80/(v-6). 1/(v+6) = 0.5/(v-6). v-6 = 0.5(v+6). v-6 = 0.5v + 3. 0.5v = 9. v = 18.

AI explanation

Let the time taken to travel downstream be t hours, making the upstream time 2t hours. Using the formula Speed = Distance / Time, the downstream speed is 80 / t and the upstream speed is 80 / 2t, which simplifies to 40 / t. We know the downstream speed is 6 km/hr faster than the boat's speed in still water, and the upstream speed is 6 km/hr slower, so (80 / t) - (40 / t) = 12. Solving 40 / t = 12 gives t = 10/3 hours. Substituting this back into the upstream speed gives 40 / (10/3) = 12 km/hr, which means the boat's speed in still water is 12 + 6 = 18 km/hr.

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