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1
Two trains of length L1 and L2 travelling at speed of S1 and S2 will cross each other in time (if they are going in opposite directions )
$$\dfrac{L_1+L_2}{S_1+S_2}$$
2
Two trains of length L1 and L2 travelling at speed of S1 and S2 will cross each other in time (if they are going in same directions )
$$\dfrac{L_1+L_2}{\left|S_1-S_2\ \right|}$$
3
If two people are running on a circular track with speeds in the ratio a:b where a and b are co-prime, then They will meet at a+b distinct points if they are running in
Opposite directions
4
If two people are running on a circular track with speeds in the ratio a:b where a and b are co-prime, then They will meet at |a-b| distinct points if they are running in
Same directions
5
If two people are running on a circular track having perimeter P, with speeds m and n,
$$\dfrac{P}{m+n}$$
6
The time for their first meeting (when they are running in opposite directions)
$$\dfrac{P}{m-n}$$
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