Question

Two trains running towards each other on parallel tracks, at speeds of 45 km/hr and 51 km/hr, take 21 seconds to cross each other. If the length of one train is 290 m, then the length (in m) of the other train is:

• A. 250
• B. 290
• C. 230
• D. 270

Answer 1

Answer:

D. 270

When two trains move towards each other, their relative speed is the sum of their speeds.

Convert speeds to m/s

$45 \text{ km/h} = \frac{45 \times 1000}{3600} = 12.5 \text{ m/s}$

$51 \text{ km/h} = \frac{51 \times 1000}{3600} = 14.1667 \text{ m/s}$

Relative speed

$12.5 + 14.1667 = 26.6667 \text{ m/s}$
$= \frac{80}{3} \text{ m/s}$

Total distance covered while crossing

$\text{Distance} = \text{Speed} \times \text{Time}$
$= \frac{80}{3} \times 21$
$= 80 \times 7 = 560 \text{ m}$

So, sum of lengths of both trains = 560 m

Find unknown length

Given one train = 290 m

$\text{Other train} = 560 - 290 = 270 \text{ m}$

Final Answer: 270 m