Final answer:
Using algebraic methods to solve for the boat's speed in still water and the current's speed, we calculated that the boat's speed is 6 mph and the current's speed is 2 mph.
Step-by-step explanation:
The subject of this question is Mathematics, specifically involving concepts of rate, time, and distance, which are part of algebra and physics.
To find the speed of the boat in still water and the speed of the current, we set up two equations using the details that it takes 2 hours to go 16 miles downstream and 4 hours to return against the current. Let b be the speed of the boat in still water and c be the speed of the current.
Going downstream, the boat's speed adds to the current's speed, so we have b + c = 16 miles / 2 hours = 8 mph. Against the current, the boat's speed subtracts the current's speed, so we have b - c = 16 miles / 4 hours = 4 mph.
Adding these two equations:
- (b + c) + (b - c) = 8 mph + 4 mph
- 2b = 12 mph
- b = 6 mph
Substituting b = 6 mph into b + c = 8 mph:
- 6 mph + c = 8 mph
- c = 2 mph
Therefore, the speed of the boat in still water is 6 mph and the speed of the current is 2 mph.
This information indicates that the correct choice from the provided options is:
- Boat speed: 6 mph; Current speed: 2 mph