Question

A train $75\text{m}$ long moving at a speed of $54\text{km/h}$ starts overtaking another train of length $125\text{m}$ moving at a speed of $36\text{km/h}$ on a parallel track. How long will the first train take to completely overtake the second train?

• A. $7.5\text{s}$
• B. $12.5\text{s}$
• C. $20\text{s}$
• D. $40\text{s}$

Answer 1

The correct option is D $40\text{s}$

Given velocity of $1^{st}$ train, $v_1=54\text{km/h}$
$\Rightarrow v_1=15\text{m/s}$
Velocity of second train, $v_2=36\text{km/h}$
$\Rightarrow v_2=10\text{m/s}$
Relative velocity, $v_{12}=v_1-v_2=5\text{m/s}$
time taken for trains to cross each other
$t=\frac{l_1+l_2}{v_{12}}=\frac{75+125}{5}=40\text{s}$