Final answer:
To find the greatest number of minutes for the return trip, we need to set up an equation based on the boat's speeds in still water and against the current. By solving this equation, we find that the boat would take 6 minutes for the return trip.
Step-by-step explanation:
To solve this problem, let's assume the speed of the boat in still water as x km/h and the speed of the current as y km/h.
According to the given information, the boat traveled against the current in 40 minutes. So, the speed of the boat in this case would be x - y km/h.
Similarly, the boat returned with the current in 6 minutes less than it would take in still water. So, the speed of the boat in this case would be x + y km/h.
Since the distance traveled is the same in both cases, we can set up an equation:
x - y = (x + y) + 6
Solving this equation, we get: x = 2y + 6
To find the greatest number of minutes for the return trip, we need to find the maximum value of x. Since x is directly proportional to y, the greatest value of x would occur when y is the smallest possible value, which is 0. Therefore, the greatest number of minutes for the return trip is 2 * 0 + 6 = 6 minutes.