Question

A boat, which moves at 18 mph in still water, travels 14 miles downstream in the same amount of time it takes to travel 10 miles upstream. Find the speed of the current.

Answer 1

Let c be the speed of the current. When traveling downstream, the boat's effective speed is 18+c mph, and when traveling upstream, the boat's effective speed is 18-c mph.

The time it takes the boat to travel 14 miles downstream is 14/(18+c) hours, and the time it takes the boat to travel 10 miles upstream is 10/(18-c) hours. Since the problem states that these times are equal, we can set up an equation:

14/(18+c) = 10/(18-c)

Now we can solve for c:

14*(18-c) = 10*(18+c)
252 - 14c = 180 + 10c
72 = 24c
c = 3

So, the speed of the current is 3 mph.