Two trains whose lengths are 450 meters and 300 meters are moving towards each other at the speed of 162 km/hr and 108 km/hr respectively. If the distance between the trains is 300... Two trains whose lengths are 450 meters and 300 meters are moving towards each other at the speed of 162 km/hr and 108 km/hr respectively. If the distance between the trains is 300 meters, then in how much time will these trains cross each other? Read more

Steps to Solve

1. Convert speeds from km/hr to m/s

   We need to convert the speeds of the trains from kilometers per hour (km/hr) to meters per second (m/s) to match the units of the lengths and distance which are in meters. To convert km/hr to m/s, we multiply by $\frac{5}{18}$.

   Train 1: $162 \text{ km/hr} = 162 \times \frac{5}{18} \text{ m/s} = 45 \text{ m/s}$ Train 2: $108 \text{ km/hr} = 108 \times \frac{5}{18} \text{ m/s} = 30 \text{ m/s}$

2. Calculate the relative speed

   Since the trains are moving towards each other, their relative speed is the sum of their individual speeds.

   Relative speed $= 45 \text{ m/s} + 30 \text{ m/s} = 75 \text{ m/s}$

3. Calculate the total distance to be covered

   The total distance the trains need to cover to completely cross each other is the sum of their lengths and the initial distance between them.

   Total distance $= 450 \text{ m} + 300 \text{ m} + 300 \text{ m} = 1050 \text{ m}$

4. Calculate the time to cross each other

   Time $= \frac{\text{Total distance}}{\text{Relative speed}}$ Time $= \frac{1050 \text{ m}}{75 \text{ m/s}} = 14 \text{ s}$