Question

Pam and Tina went for a 12 mile hike (round trip) to the top of a mountain. It took 5 hours. They were able to hike 1 mile per hour faster on the way down. How fast did they hike going up the mountain

Answer 1

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.