Arithmetic

Time, Speed & Distance

Medium

Two trains of equal length are running from the same origin on parallel tracks in the same direction, at the speeds of 58 km/hr and 73 km/hr, respectively. The faster train passes the other train in 144 seconds. What is the length (in meters) of each train?

344 m

262 m

300 m

240 m

✅ Correct Option: 3

Two trains of equal length are running in the same direction on parallel tracks. The slower train travels at 58 km/hr and the faster train travels at 73 km/hr.

Since both trains move in the same direction, the relative speed determines how fast the faster train gains on the slower train.

Relative Speed $= 73 - 58 = 15$ km/hr

The time is given in seconds and the answer is needed in meters, so the speed must be converted to m/s.

To convert km/hr to m/s, multiply by $\frac{5}{18}$ :

$15 \times \frac{5}{18}$

$= \frac{75}{18}$

$= \frac{25}{6}$ m/s

When the faster train completely passes the slower train, it must cover the length of both trains. Since both trains have equal length $L$ :

Total distance covered $= L + L = 2L$

Using the relationship between distance, speed, and time:

$2L = \frac{25}{6} \times 144$

$2L = \frac{25 \times 144}{6}$

$2L = \frac{3600}{6}$

$2L = 600$

$L = 300$ meters

Therefore, each train is 300 meters long.

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