Problema Solution
Tina hiked 15 km up a mountain trail. Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1 km/h. How long did it take her to climb up and down the mountain.
Answer provided by our tutors
the climb down is faster, therefore:
rate down - rate up = 1 km/h
time to climb up: t hours
distance = 15 km
rate up = 15 / t
rate down = 15 / (t-0.5)
this gives the equation:
15/(t-0.5) - 15/t = 1
solving for 't' gives a positive answer of 3 hours
The climb up was 3 hours, the climb down was then 2.5 hours.