Question

Two trains of equal length are running on parallel lines in the same direction at speeds of 90 km/h and 51 km/h. The faster train passes the slower train in 36 seconds. The length of each train is:

• A. 207 meters
• B. 199 meters
• C. 195 meters
• D. 186 meters

Answer 1

Answer:

C. 195 meters

The length of each train is 195 meters.

• Find the relative speed:
  Since the trains are moving in the same direction, subtract their speeds.
  $\text{Relative Speed} = 90\text{ km/h} - 51\text{ km/h} = 39\text{ km/h}$

• Convert the speed to meters per second (m/s):
  Multiply by $\frac{5}{18}$ to convert from km/h to m/s.
  $\text{Relative Speed} = 39 \times \frac{5}{18} = \frac{195}{18}\text{ m/s}$

• Calculate the total distance covered:
  Distance is speed multiplied by time.
  $\text{Total Distance} = \frac{195}{18}\text{ m/s} \times 36\text{ seconds} = 195 \times 2 = 390\text{ meters}$

• Determine the length of each train:
  When one train passes another, the total distance covered is the sum of their lengths ($L + L = 2L$).
  $2L = 390\text{ meters}$
  $L = \frac{390}{2} = 195\text{ meters}$