#### Answer

The required distance between the two mountains is $15,000~km$. Since the required distance is even more than the Earth's diameter, this is not feasible.

#### Work Step by Step

Let $d$ be the required distance between the two mountains. The total time for the light to travel twice this distance plus the friend's reaction time is $0.35~s$. Since the friend's reaction time is $0.25~s$, the time for the light to travel twice this distance is $0.10~s$. We can find $d$:
$2d = c~(0.10~s)$
$d = \frac{(3.0\times 10^8~m/s)~(0.10~s)}{2}$
$d = 1.5\times 10^7~m$
$d = 15,000~km$
The required distance between the two mountains is $15,000~km$. Since the required distance is even more than the Earth's diameter, this is not feasible.