Question

Two trains $130$ m and $110$ m long are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in $3$ seconds. Find the speed of each train?

• A. $38$ m/s, $36$ m/s
• B. $42$ m/s, $38$ m/s
• C. $36$ m/s, $42$ m/s
• D. $40$ m/s, $36$ m/s

Answer 1

Answer: (B)

$42$ m/s, $38$ m/s

Let the speeds of the faster train be $x$ m/s and that of the slower train be $y$ m/s.
When the two trains are moving in the same direction:
Relative speed $=(x-y)$ m/s

$\therefore$ $\frac{130m+110m}{x-y}=60$
$\Rightarrow \frac{240}{x-y}=60$

$\Rightarrow x-y=4$ .... (i)

When the two trains are moving in opposite direction:
Relative speed $=(x+y)$ m/s

$\therefore \frac{130m+110m}{x+y}=3\Rightarrow x+y=80$ .... (ii)
Adding eqn (i) and (ii), we get

$2x=84$

$\Rightarrow$ $x=42$ m/s
$\therefore$ putting value of $x$ in (i), we get

$y=38$ m/s.