Answer:
The speed of the current is 4 mph.
Explanation:
The speed of the boat in still water is 12 mph, but when it's going against the stream it is "12 - x" mph and when it's going with the stream it is "12 + x" mph. Since the total trip took 15 h, then the sum of the times from each leg of the trip must be equal to that value. Using the average speed formula, we can manipulate it to give us the time of each leg as shown below:
speed = distance / time
time*speed = distance
time = distance / speed
For the downstream:
time 1 = 80 / (12 + x)
For the upstream:
time 2 = 80 / (12 - x)
The sum of these two times must be equal to 15 h, therefore:
15 = [80 / (12 + x)] + [80 / (12 - x)]
15 = [80*(12 - x) + 80*(12 + x)]/[(12+x)*(12-x)]
15 = {80*[(12 - x) + (12 + x)]}/[12² - x²]
15 = {80*[12 + 12 -x + x]}/(144-x²)
15 = (80*24)/(144 - x²)
15 = 1920/(144 - x²)
15*(144 - x²) = 1920
2160 - 15x² = 1920
-15x² = 1920 -2160
-15x² = -240
x² = -240 / -15 = 16
x = 4 or x = -4
Since the speed can't be negative in this context, the speed of the current is 4 mph.