Erica hiked up a mountain trail at 3 km/h and returned at 4 km/h. The entire trip took 5 hours 10 minutes, including the half hour she spent at the top. How long was the trail?

Question

anonymous · Answer

$$\text{up:}\; d=3t_1\\text{down:}\;d=4t_2\t_1+t_2+{1\over2}=5+{10\over60}\
t_1+t_2=5+{1\over6}-{1\over2}={28\over6}={14\over3}\
3t_1=4t_2=4\left({14\over3}-t_1\right)\
3t_1={56\over3}-4t_1
$$

anonymous · Answer

solve t1 from there
then use the equation for "d" going up

anonymous · Answer

that "d" is you one way distance.. (I think it should be 8km one way)