Stu hiked a trail at an average rate of 3 miles per hour. he ran back on the same trail at an average rate of 5 miles per hour. he traveled for a total of 3 hours. the equation 3t = 5(3 – t) can be used to find the time it took stu to hike one way. how long did it take stu to hike the trail one way? how long is the trail? what is the total distance stu hiked?

Let d =  the length of the trail, miles

Note that
distance = speed * time
or
time = distance / speed.

The time, t₁, to travel the trail at 3 miles per hour is
t₁ = d/3 hours
The time, t₂, to travel back at 5 miles per hour is
t₂ = d/5 hours

Because the total time is 3 hours, therefore
t₁ + t₂ = 3
d/3 + d/5 = 3
d(1/3 + 1/5) = 3
d(8/15) = 3
Multiply each side by 15.
8d = 3*15 =45
d = 45/8 = 5 5/8 miles or 5.625 miles
Total distance = 2*d = 11.25 miles or 11 1/4 miles.

t₁ = 5.625/3 = 1.875 hours or 1 hour, 52.5 minutes
t₂ = 5.625/5 = 1.125 hours or 1 hour , 7.5 minutes

Answers ;
Time to travel at 3 miles per hour = 1.875 hours (1 hour, 52.5 minutes)
Time to return at 5 miles per hour = 1.125 hours (1 hour, 7.5 minutes)
Total distance traveled = 2*d = 11.25 miles.