A bicyclist rode up a mountain road at 12 kmh and then back

A bicyclist rode up a mountain road at 12 km/h and then back down 30 km/h. If the round trip took 3.5 h, how long did the ride up the mountain take?

Solution

distance (d)=rate (r)*time(t) -->> d=rt
Let the time (t) up the mountain be: t
Then the rest of the 3.5 hrs is the time to get down: (3.5-t)
Then the distance up is: 12t
and the distance down is: 30(3.5-t)
The distance up a mountain is the same as the distance down so:
12t=30(3.5-t)
12t=105-30t
12t+30t=105-30t+30t
42t=105
42t/42=105/42
t=2.5
***The trip up the mountain took: t=2.5 hrs