Multiple choice

A boat takes $6$ hours to travel $8\ km$ upstream and $32\ km$ downstream and it takes $7$ hours to travel $20\ km$ upstream and $16\ km$ downstream. Find the speed of the boat in still water and the speed of the stream.

  1. $6,2$
  2. $6,1$
  3. $6,7$
  4. $6,9$
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A Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 8/u + 32/v = 6 and 20/u + 16/v = 7. Solving this system gives u = 4 and v = 8. Speed of boat = (v + u)/2 = 6, speed of stream = (v - u)/2 = 2.

AI explanation

Let the upstream speed be x and the downstream speed be y. The equations are 8/x + 32/y = 6 and 20/x + 16/y = 7. Multiplying the first equation by 2 gives 16/x + 64/y = 12, and multiplying the second by 5 gives 100/x + 80/y = 35. Multiplying the first new equation by 5 and the second by 4 yields 80/x + 320/y = 60 and 400/x + 320/y = 140. Subtracting them gives 320/x = 80, so x = 4. Substituting x into the first original equation gives 2 + 32/y = 6, so y = 8. The speed of the boat in still water is (4 + 8) / 2 = 6, and the speed of the stream is (8 - 4) / 2 = 2. The result is 6, 2.

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