Final answer:
The speed of the boat in still water is calculated by averaging the boat's upstream speed and the boat's downstream speed. By denoting the speed of the boat in still water as ‘b’, and the speed of the current as ‘c’, we have the equations (60 km / b - c) + (100 km / b + c) = 8 hours and (75 km / b - c) + (175 km / b + c) = 12 hours. Solving these equations will give us ‘b’.
Step-by-step explanation:
In this problem, we are considering the speed of the boat in upstream and downstream. The speed in still water would be the average of the boat's upstream speed and the boat's downstream speed.
Let's denote the speed of the boat in still water as ‘b’, and the speed of the current as ‘c’. When the boat is going upstream, it's moving against the current, so the effective speed is ‘b - c’. When the boat is going downstream, it's moving with the current, so the effective speed is ‘b + c’.
From the given information, we have the following two systems of equations:
- (60 km / b - c) + (100 km / b + c) = 8 hours
- (75 km / b - c) + (175 km / b + c) = 12 hours
By solving these equations, we can find the speed of the boat in still water (‘b’).
Learn more about Boat Speed