Answer:
Approximately [tex]365\; {\rm m}[/tex].
Explanation:
Let [tex]d[/tex] denote the distance between the hikers and the mountain.
The sound wave from the hikers need to travel a distance of [tex]d[/tex] to reach the mountain. The echo comes back at the hikers almost immediately after that and would need to travel the same distance, [tex]d\![/tex], to reach the hikers.
Hence, the [tex]t = 2.10\; {\rm s}[/tex] between the shout and the echo is the time it takes for sound to travel a distance of [tex]2\, d[/tex]- twice the distance between the hikers and the mountain.
Distance that sound travels in [tex]t = 2.10\; {\rm s}[/tex]:
[tex]\begin{aligned} s &= v\, t \\ &= 348\; {\rm m\cdot s^{-1}} \times 2.10\; {\rm s} \\ &= 730.8\; {\rm m} \end{aligned}[/tex].
The distance [tex]d[/tex] between the hikers and the mountains would be:
[tex]\begin{aligned} d &= \frac{s}{2} \\ &= \frac{730.8\; {\rm m}}{2} \\ &\approx 365\; {\rm m}\end{aligned}[/tex].
