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?
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.