Final answer:
The speed of the boat in still water is 13 mph, derived by setting up an equation based on the times to travel upstream and downstream, given the speed of the current and the distances traveled.
Step-by-step explanation:
To solve this problem, we need to determine the speed of the boat in still water. We know the speed of the current in the river is 4 mph, so when the boat travels downstream, its effective speed increases by the speed of the current; and when it travels upstream, its effective speed decreases by the speed of the current.
Let's denote the speed of the boat in still water as x mph. Therefore, the speed of the boat going downstream is (x + 4) mph and upstream is (x - 4) mph.
Since the time to travel downstream for 17 miles is the same as the time to go 9 miles upstream, we can write the equation based on the time it takes to travel these distances at the respective speeds:
Time downstream = Distance downstream / Speed downstream = 17 / (x + 4)
Time upstream = Distance upstream / Speed upstream = 9 / (x - 4)
Since Time downstream = Time upstream, we get the equation:
17 / (x + 4) = 9 / (x - 4)
By solving this equation for x, we can find the speed of the boat in still water:
17(x - 4) = 9(x + 4)
17x - 68 = 9x + 36
17x - 9x = 36 + 68
8x = 104
x = 13 mph
Therefore, the speed of the boat in still water is 13 mph.