How many miles?

Question

Without taking a single break, Mercedes hiked for 10 hours, up a mountain and back down by the same path. While hiking, she averaged 2 miles per hour on the way up and 3 miles per hour on the way down. How many miles was it from the base of the mountain to the top?

Answer 1

 

 

12 miles

 

 

Distance = Rate x time

 

 Same Distance going up and down.

 

    2 mph x time going up  =  3 mph x Time going down

 

    Time going up + time going down = 10

 

    

Let T_up = time going up and T_down = time going down.

 

  2* t_up = 3 * t_down  -->   t_up = 3/2 * t_down = 1.5 * t_down

 

  t_up + t_down = 10

 

Substituting the first equation into the second:

 

 1.5 * t_down + t_down = 10

 

2.5*t_down = 10

 

t_down = 4 hours ---->  t_up = 10 - 4 = 6

 

Going up:  2 miles per hour for 6 hours = 12 miles

Going down: 3 miles per hour for 4 hours = 12 miles 

 

CONCLUSION: The mountain is 12 miles high