Kabir climbs up a hill at a speed of 3 miles per hour and comes down at 5 miles per hour. If the total time taken for the total journey is 10 hours, then what was the distance between hill top and foothills?

18.75 miles

distance = speed x time 

When the distance is same,

Ratio of speed ∝ $\frac{1}{ratio\; of \;time}$

                 Uphill   :    Downhill

Speed         3        :      5

Time           5        :      3 

Total time = 10 hrs  = 8R

               ⇒   R = $\frac{10}{8}$   

Distance on one side = speed x time

                               = 3 x 5R  (during uphill)  

                               = 3 x 5 $\frac{10}{8}$   

                               = 18.75 miles