The speed of a stream is 5 mph. A boat travels 10 miles upstream in the same time it takes to travel 20 miles downstream. What is the speed of the boat in still water?

Answer 1

Let the speed of the boat in still water be x mph.
Then, the speed of the boat downstream (with the stream) is (x+5) mph.
The speed of the boat upstream (against the stream) is (x-5) mph.

Given that the boat travels 10 miles upstream in the same time it takes to travel 20 miles downstream, we can set up the following equation to represent this situation:

10/(x-5) = 20/(x+5)

Cross-multiplying, we have:

10(x+5) = 20(x-5)

10x + 50 = 20x - 100

Subtracting 10x from both sides, we have:

10x - 10x + 50 = 20x - 10x - 100

50 = 10x - 100

Adding 100 to both sides, we have:

50 + 100 = 10x - 100 + 100

150 = 10x

Dividing both sides by 10, we have:

150/10 = 10x/10

15 = x

Therefore, the speed of the boat in still water is 15 mph.