Q.A man standing between 2 parallel cliffs fires a gun. He hears two echoes one after 3 seconds and other after 5 seconds. The separation between the two cliffs is 1360 m, what is the speed of sound?

[!TLDR] With distances a=1.5v and b=2.5v to the two cliffs (from the 3 s and 5 s echo delays) summing to 1360 m, …

Let the man be a distance $a$ from the nearer cliff and $b$ from the farther cliff, with $a+b=1360$ m (the separation between the two cliffs). The echo from the NEARER cliff returns after 3 s, so the round trip to it and back covers $2a=v\times3\Rightarrow a=1.5v$. The echo from the FARTHER cliff returns after 5 s, so $2b=v\times …

Express each cliff's distance in terms of v using its own round-trip echo delay (distance = v×time/2), then use the fact the two di …

Using only ONE of the two echo delays (e.g. just the 3 s one) to find v directly, instead of recognising that BOTH delays and the given cliff se …