The speed of the current in a river is 6 mph. A ferry
operator who works that part of the river is looking to buy a new boat for his business.
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours.
He has a boat in mind, but he can only test it on a lake where there is no current.
How fast must the boat go on the lake in order for it to serve the ferry operator's needs?
Let x be the speed of the boat in still water.
Against the current, the effective speed of the boat is (x - 6) mph.
With the current, the effective speed of the boat is (x + 6) mph.
Since the distance to travel is 22.5 miles each way, the total distance is 45 miles.
The time taken to travel the distance against the current is 22.5 / (x - 6) hours.
The time taken to travel the distance with the current is 22.5 / (x + 6) hours.
According to the ferry operator's needs, the total time taken for the round trip must be 9 hours.
Therefore, 22.5 / (x - 6) + 22.5 / (x + 6) = 9.
Solving this equation will give us the value of x, the speed of the boat in still water.