Sam hiked up a mountain at a rate of 25 mph and returned alo

Sam hiked up a mountain at a rate of 2.5 mph and returned along the same path at a rate of 3 mph. His total hiking time was 11hr. How long was the hiking trail?

Solution

The distance traveled at 2.5 mph=the distance traveled at 3mph
the total time for the entire trip is 11 hours
x=time to hike up the mountain at 2.5 mph
11-x=time to hike down the mountain
Rate*Time=Distance
2.5x=3(11-x)
use the distributive property
2.5x=33-3x
add 3x to both sides
5.5x=33
divide both sides by 5.5
x=6
It takes 6 hours to hike up the mountain
Distance=2.5*6=15 miles is the length of the hiking trail.
Let\'s double check our answer
2.5*6=3*5
15=15