SOLUTION: The speed of a stream is 3 mph. A boat travels 8 miles upstream at the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?

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Question 153431: The speed of a stream is 3 mph. A boat travels 8 miles upstream at the same time it takes to travel 14 miles downstream. What is the speed of the boat in still water?
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the speed of the boat in still water.
So
The boat's downstream speed relative to the riverbank is x+3.
The boat's upstream speed relative to the riverbank is x-3.
Time spend traveling downstream is 14%2F%28x%2B3%29
Time spend traveling upstream is 8%2F%28x-3%29
As the time spend traveling downstream is the same as the time spend traveling upstream, we have:
14%2F%28x%2B3%29=8%2F%28x-3%29
Solving for x, we have:
%28x%2B3%29%28x-3%29%2A%2814%2F%28x%2B3%29%29=%28x%2B3%29%28x-3%29%2A%288%2F%28x-3%29%29 (multiply both side by (x+3)(x-3)
14%28x-3%29=8%28x%2B3%29
14x-42=8x%2B24
6x=66
x=66%2F6
x=11
So the speed of the boat in still water is 11 miles per hour.