A train $A$ which is 120 m long is running with velocity $20 \mathrm{~m} / \mathrm{s}$ while train $

Question

A train $A$ which is 120 m long is running with velocity $20 \mathrm{~m} / \mathrm{s}$ while train $B$ which is 130 m long is running in opposite direction with velocity $30 \mathrm{~m} / \mathrm{s}$. What is the time taken by train $B$ to cross the train $A$ ?

Professor PC Thomas Classes · Answer

(a): Length of train $A=120 \mathrm{~m}$ Velocity of train $A, v_A=20 \mathrm{~m} / \mathrm{s}$ Length of train $B=130 \mathrm{~m}$ Velocity of train $B, v_B=30 \mathrm{~m} / \mathrm{s}$ Relative velocity of $B$ w.r.t. $A=v_B+v_A=50 \mathrm{~m} / \mathrm{s}$ (trains move in opposite directions) Total path length to be covered by $B=130+120=250 \mathrm{~m}$ ∴ Time taken by train $B=\frac{250 \mathrm{~m}}{50 \mathrm{~m} / \mathrm{s}}=5 \mathrm{~s}$