Multiple choice

The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?

  1. 10 kmph

  2. 21 kmph

  3. 8 kmph

  4. 12 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be boat speed. Downstream speed = v+4, upstream = v-4. 6/(v+4) + 6/(v-4) = 2. 3/(v+4) + 3/(v-4) = 1. 3(v-4 + v+4) = v^2 - 16. 6v = v^2 - 16. v^2 - 6v - 16 = 0. (v-8)(v+2) = 0. v = 8.

AI explanation

Using the total time formula for a round trip where the boat speed in still water is b, we have 6/(b-4) + 6/(b+4) = 2. Multiplying by (b-4)(b+4) gives 6b + 24 + 6b - 24 = 2(b^2 - 16), which simplifies to 12b = 2b^2 - 32 or b^2 - 6b - 16 = 0. Factoring this quadratic equation yields (b-8)(b+2) = 0, and since speed must be positive, b is 8 kmph.

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