Answer:
54 mph
Step-by-step explanation:
Let s represent the average speed on the way to the lodge. The relation between time, speed, and distance is ...
time = distance/speed
so, the travel time to the lodge is 1080/s. The travel time on the return is 1080/(s-6). The difference in times is then ...
1080/(s-6) -1080/s = 2.5
1080s -1080(s-6) = 2.5(s)(s -6) . . . . multiply by s(s-6)
Now, we have a quadratic that can be solved in any of the usual ways.
2.5s² -15s -6480 = 0 . . . . . . . . . . . . subtract the left side
s² -6s -2592 = 0 . . . . . . . . . . . . . . . . divide by 2.5
(s² -6s +9) -(2592 +9) = 0 . . . . . . . . complete the square
(s -3)² = 51² . . . . . . . . . . . . . add 2601, write as squares
s = 3 + 51 = 54 . . . . . . . . . . positive square root, add 3
The average speed on the way to the lodge was 54 mph.
