# Problems on Trains Formulas

Commit to memory the following tips for solving trains questions easily.

Key concepts:
1.  If two objects are moving in opposite directions towards each other at speeds $u$ and $v$, then
Relative speed = Speed of first + Speed of second = $u + v.$

2. If the two objects move in the same direction with speeds u and v, then
Relative speed = difference of their speeds = $u - v$.

Important Models:
Model 1. one Pole and one Train:

Length of The Train (m) = Speed of the Train (m/s) × Time taken to cross the pole (s)
Formula: $L = v \times t$

Model 2. one Train and one Bridge:

Length of the Train + Length of the Bridge (m) = Speed of the Train (m/s) × Time taken to cross the bridge(s)
Formula: ${L_1} + {L_2} = v \times t$

Model 3. one Train with speed speed $u$ and one moving person with speed $v$
Case 1: If both are moving in same direction

Length of The Train (m) = [Speed of the Train - Speed of the Man] (m/s) × Time taken to cross the man (s)
Formula: $L = \left( {u - v} \right) \times t$

Case 2: If both are moving in opposite direction

Length of The Train (m) = (Speed of the Train + Speed of the Man) (m/s) × Time taken to cross the man (s)
Formula: $L = \left( {u + v} \right) \times t$

Model 4. 2 Trains with speeds $v$, $u$
Case 1: If both are moving in same direction

(Length of The Train 1 + Length of the Train 2)(m) = (Speed of the Train1 - Speed of the Train 2) (m/s) × Time taken to cross (s)
Formula: ${L_1} + {L_2} = \left( {u - v} \right) \times t$

Case 2: If both are moving in opposite direction

(Length of The Train 1 + Length of the Train 2)(m) = (Speed of the Train1 + Speed of the Train 2) (m/s) ×  Time taken to cross (s)
Formula: ${L_1} + {L_2} = \left( {u + v} \right) \times t$