Question

A boat traveled 140 kilometers each way downstream and back. The trip downstream took 5 hours. The trip back took 14 hours. Find the speed of the boat in still water and the speed of the current.

Answer 1

Explanation:

Assuming 280 miles is the total distance travelled:

Let b = boat speed in still water

Let c = current speed.

For the downstream trip the speed is b + c. In 7 hours at the speed of (b + c) mph the boat travels 140 miles.

7(b + c) = 140 .............(1)

For the upstream trip the speed is b - c. In 14 hours at the speed of (b - c) mph the boat travels 140 miles.

14(b - c) = 140 ............(2)

The left hand sides of equations (1) and (2) are equal. Therefore we can write

7b + 7c = 14b - 14c ...........(3)

Rearranging equation (3) we get

21c = 7b

c = b/3 .......................(4)

The value for c obtained in equation (4) should now be substituted into equation (1) which can then be solved to find the value of b.

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