A train completely overtakes two persons, walking in the same direction with speeds 3 km/hr and 4 km/hr in 9 seconds and \(\frac{75}{8}\) seconds respectively. What is the length of the train?

Formula used:

Distance = Speed × Time

Concept used:

1. While a train crosses a person, it covers a distance equal to its length.

2. When two objects move in the same direction,

Relative speed = Speed₁ - Speed₂

3. Km/h = 5/18 m/sec

Calculation:

Let the speed of the train be 'x' km/h and the length of the train be 'L'

According to the question, overtakes 2 persons, walking in the same direction with speeds of 3 km/h & 4 km/h in 9 sec & 75/8 sec

Here, the distance covered is the length of the train

⇒ (x - 3) × 9/3600 = (x - 4) × 75/3600

⇒ (x - 3) × 9 = (x - 4)× 75/8

⇒ 24x - 72 = 25x - 100

⇒ x = 28 km/h

Length of train = [(x - 3) × 9/3600] km

⇒ Length of train = (28 - 3) × 1/400 km

⇒ Length of train = 25/400 = 1/16 km = 1/16 × 1000 = 62.5 m

∴ The length of the train is 62.5 m.