Answer:
15 mph
Explanation:
Let's call the speed of the boat in still water "b" (in mph).
When the boat travels upstream (against the current), its effective speed is reduced by the speed of the stream, so its speed relative to the shore is b - 5 mph. When the boat travels downstream (with the current), its effective speed is increased by the speed of the stream, so its speed relative to the shore is b + 5 mph.
We know that the time it takes to travel 10 miles upstream is the same as the time it takes to travel 20 miles downstream. Let's call this common time "t" (in hours).
Using the formula speed = distance / time, we can set up the following equations:
10 / (b - 5) = t
20 / (b + 5) = t
Now we can solve for "b".
From the first equation, we can solve for "t":
t = 10 / (b - 5)
We can substitute this into the second equation:
20 / (b + 5) = 10 / (b - 5)
Simplifying this equation gives:
2(b - 5) = b + 5
2b - 10 = b + 5
b = 15 mph
Therefore, the speed of the boat in still water is 15 mph.