Question

Two trains having lengths of 170 m and 480 m are running at speeds of 70 km/h and 80 km/h, respectively, in the same direction. The time taken (in minutes) by the faster train, coming from behind, to completely cross the other train is:

• A. 4
• B. 4.2
• C. 5
• D. 3.9

Answer 1

Answer:

D. 3.9

Since the trains are moving in the same direction, use relative speed.

Total distance to be covered

$170 + 480 = 650 \text{ m}$

Relative speed

$80 - 70 = 10 \text{ km/h}$

Convert to m/s:

$10 \times \frac{5}{18} = \frac{25}{9} \text{ m/s}$

Time taken

$\text{Time}=\frac{650}{25/9}$
$=650 \times \frac{9}{25}$
$=234 \text{ seconds}$

Convert seconds to minutes:

$\frac{234}{60}=3.9 \text{ minutes}$

So, the required time is:

$\boxed{3.9 \text{ minutes}}$