- Erica hiked up a mountain trial at 3km/h and returned at 4k/h. The entire trip took five hours 10 min including the half an hour she spent at the top. How long was the trial?
Let the mountain trail be x km
Time taken to go up = x/3 hours
time taken to return = x/4 hours
rest time = 1/2 hours
total time = 5 h 10 m = 5 1/6 h = (5*6+1)/6 =(31/6)hrs
i.e x/3 + x/4 +1/2 = 31/6
(x/3 + x/4) = 31/6 - 1/2
Making all of them like fractions, (LCM of 4,3,6,2 = 12)
(4*x/4*3) + (3*x/3*4) = (2*31/2*6) - (6*1/6*2)
4x/12 + 3x/12 = 62/12-6/12
(4x+3x)/12 = (62-6)/12
7x/12 = 56/12
7x = 56 (multiplying both sides by 12)
x = 56/7 = 8 km
The mountain trrail is 8 km