Question

A 280 m long train overtakes a man moving at a speed of 5 km/h (in same direction) in 42 seconds. How much time (in seconds) will it take this train to completely cross another 500 m long train, moving in the opposite direction at a speed of 43 km/h?

• A. 52
• B. 34
• C. 39
• D. 38

Answer 1

Answer:

C. 39

The time required for the train to completely cross the second train is 39 seconds.

1. Find the Speed of the First Train

• When a train crosses a man, the distance covered is equal to the length of the first train ($280\text{ m}$).

• $\text{Relative Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{280\text{ m}}{42\text{ s}} = \frac{20}{3}\text{ m/s}$

• Convert this speed from $\text{m/s}$ to $\text{km/h}$ by multiplying by $\frac{18}{5}$:
  $\text{Relative Speed} = \frac{20}{3} \times \frac{18}{5} = \mathbf{24\text{ km/h}}$

• Since the train and the man are moving in the same direction, subtract their speeds to get the relative speed:
  $\text{Relative Speed} = \text{Speed of Train}_1 - \text{Speed of Man}$
  $24\text{ km/h} = \text{Speed of Train}_1 - 5\text{ km/h} \implies \text{Speed of Train}_1 = \mathbf{29\text{ km/h}}$

2. Calculate Time Taken to Cross the Second Train

• When the two trains cross each other in opposite directions, add their lengths to find the total distance:
  $\text{Total Distance} = 280\text{ m} + 500\text{ m} = \mathbf{780\text{ m}}$

• Add their speeds to find the total relative speed:
  $\text{Total Relative Speed} = 29\text{ km/h} + 43\text{ km/h} = \mathbf{72\text{ km/h}}$

• Convert this total relative speed back into $\text{m/s}$ by multiplying by $\frac{5}{18}$:
  $\text{Total Relative Speed} = 72 \times \frac{5}{18} = \mathbf{20\text{ m/s}}$

• Calculate the final time required:
  $\text{Time} = \frac{\text{Total Distance}}{\text{Total Relative Speed}} = \frac{780\text{ m}}{20\text{ m/s}} = \mathbf{39\text{ seconds}}$