Final answer:
The fisherman rowed a total distance of 20/3 miles during the entire trip.
Step-by-step explanation:
To determine how far the fisherman rowed during the entire trip, we need to consider the time he spent rowing in each direction. Let's assume that the distance he rowed upstream is x miles. Since he was rowing at a speed of 1 mph, it took him x hours to row upstream. This means that the distance downstream would also be x miles, as he rowed at a speed of 4 mph in that direction. Since the total trip took 5 hours, he spent 5 - x hours rowing downstream. To calculate the total distance, we add the distance upstream and downstream:
Total distance = distance upstream + distance downstream = x miles + x miles = 2x miles
Now, let's solve for x by setting up an equation using the time spent for each leg of the trip:
Time to row upstream = Distance upstream / Speed upstream = x / 1 = x hours
Time to row downstream = Distance downstream / Speed downstream = x / 4 = 5 - x hours
By solving the equation: x / 4 = 5 - x, we find x = 10/3. Plugging this value back into the equation for the total distance, we get:
Total distance = 2 * x = 2 * (10/3) = 20/3 miles