Final answer:
To determine the boat's speed and the current's speed, two equations are set up based on the distances and times given, then solved simultaneously to find that the boat's speed is 5 mph, and the current's speed is 1 mph.
Step-by-step explanation:
Finding Speed of the Boat and Current
To find the speed of the boat and the speed of the current, we can set up a system of equations. Let b represent the speed of the boat in still water, and c represent the speed of the current. When traveling with the current, the effective speed of the boat is b+c, and against the current, it is b-c.
The boat travels 12 miles with the current in 2 hours, so the equation for this is:
(b+c) × 2 = 12
Similarly, the boat travels 12 miles against the current in 3 hours, leading to the equation:
(b-c) × 3 = 12
By solving this system of equations, we find that the boat's speed is 5 mph and the current's speed is 1 mph.
This is an algebraic method for solving real-world problems involving motion.