Answer:
2 mph
Step-by-step explanation:
The relationship between time, speed, and distance is ...
time = distance/speed
If s is the speed going up the mountain, then s+1 is the speed coming down. The total trip time for 6 miles up and 6 miles down is ...
6/s +6/(s+1) = 5
6(s+1) +6s = 5(s)(s+1)
5s^2 -7x -6 = 0 . . . . subtract the left side, simplify to standard form
(s -2)(5s +3) = 0 . . . . factor
s = 2 or -3/5 . . . . values that make the factors 0
Their speed was 2 miles per hour going up the mountain.
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Check
It took 6/2 = 3 hours to go up the mountain, and 6/(2+1) = 2 hours to come down, for a total of 5 hours.
