Eruca hiked up a mountain trail at 3 kmhr and returned home

Eruca hiked up a mountain trail at 3 km/hr and returned home at 4 km/hr. The entire trip took 5 hrs and 10 minutes. How long was the trail?

Solution

Up DATA:
rate = 3 km/hr ; time = x hrs ; distance = 3x km
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Down DATA:
rate = 4 km/hr ; time = (5 1/6)-x hrs ; distance = 4[(31/6) -x] km
===========================
Equation:
distance up = distance down
3x = 4[(31/6)-x]
3x = (124/6) - 4x
7x = 124/6
x = 124/42
x = 2.95.. hrs
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Distance = 3x = 8.86.. km