Final answer:
The boat's speed in calm water is 6 mph and it traveled 9 miles one way.
Step-by-step explanation:
To find the boat's speed in calm water, we need to analyze the information given. During the first leg of the trip, the boat is traveling with the current, so the effective speed is the sum of the boat's speed in calm water and the current's speed. Using the formula speed = distance / time, we can set up the equation 3 mph = distance / 3 hours and solve for the distance. We find that the boat traveled 9 miles one way.
During the second leg of the trip, the boat is traveling against the current, so the effective speed is the difference between the boat's speed in calm water and the current's speed. Using the same formula, we can set up the equation 3 mph = distance / 4 hours and solve for the distance again. We find that the boat also traveled 12 miles on the return trip.
Now, to find the boat's speed in calm water, we can equate the effective speed for both legs of the trip. Let x be the boat's speed in calm water. For the downstream leg, we have x + 3 = 9/3, and for the upstream leg, we have x - 3 = 12/4. Simplifying these equations, we find x = 6 mph. Therefore, the boat's speed in calm water is 6 mph.