Final answer:
The boat's speed in still water is 10 mph, and the current's speed is 5 mph. This was calculated using the given downstream and upstream speeds of the boat, revealing the correct answer to be C) Boat: 10 mph, Current: 5 mph.
Step-by-step explanation:
To determine the speed of the current and the speed of the boat if there were no current, you can use the speeds of the boat traveling downstream and upstream. When the boat is traveling downstream, the current aids its motion, so the boat's speed is the sum of its own speed in still water and the speed of the current. Conversely, when traveling upstream, the boat's speed is reduced by the speed of the current.
Let's denote the boat's speed in still water as b and the speed of the current as c. Going downstream, the boat's speed is b + c = 15 mph. Upstream, the boat's speed is b - c = 5 mph. Adding these two equations, we get:
2b = 15 mph + 5 mph
2b = 20 mph
b = 10 mph
Now, finding the speed of the current, we substitute the value of b into one of the original equations:
b + c = 15 mph
10 mph + c = 15 mph
c = 15 mph - 10 mph
c = 5 mph
Therefore, the speed of the boat in still water would be 10 mph, and the speed of the current is 5 mph. The correct answer is C) Boat: 10 mph, Current: 5 mph.