Abhishek climbs up a hill at a speed of 3 mi/h and comes down at a speed of 5 mi/h. If the total time taken for the two-way journey is 10 hours, then what is the distance between the hilltop and the foothill?

Let's assume the distance of a one-way journey is 'd' mi.

If the total time taken for the two-way journey is 10 hours.

Let's assume the time taken while climbs up is 't' hours.

time taken while comes down = (10-t) hours

Abhishek climbs up a hill at a speed of 3 mi/h.

$$speed = \frac{distance}{time}$$

$$3 = \frac{d}{t}$$

$$t = \frac{d}{3}$$    Eq.(i)

Comes down at a speed of 5 mi/h.

$$5 = \frac{d}{(10-t)}$$

$$10-t = \frac{d}{5}$$

$$10-\frac{d}{5} = t$$    Eq.(ii)

So equating Eq.(i) and Eq.(ii).

$$\frac{d}{3} = 10-\frac{d}{5}$$

$$\frac{d}{3}+\frac{d}{5}=10$$

$$\frac{8d}{15}=10$$

$$d=\frac{150}{8}$$

Distance between the hilltop and the foothill = d = 18.75 mi