Two trains 85 m and 75 m long are running in the same direction on parallel tracks with speeds of 62 km/h and 44 km/h respectively. In how many seconds will the faster train completely cross the slower train?

Introduction / Context:
This problem deals with relative speed of two trains moving in the same direction on parallel tracks. When one train overtakes another, it must cover the combined length of both trains relative to the other train. The question checks your understanding of effective relative speed, conversion of units, and time calculation when two moving objects are involved.

Given Data / Assumptions:
- Length of the first (faster) train = 85 m.
- Length of the second (slower) train = 75 m.
- Speed of the first train = 62 km/h.
- Speed of the second train = 44 km/h.
- Both trains move in the same direction on parallel tracks at constant speeds.
- We need the time for the faster train to completely cross the slower one, in seconds.

Concept / Approach:
When two trains move in the same direction, the relative speed is the difference of their speeds. For the faster train to fully overtake the slower train, it must cover a distance equal to the sum of both train lengths relative to the slower train. We convert the relative speed from km/h to m/s and then apply time = distance / speed to get the result in seconds.

Step-by-Step Solution:
Step 1: Compute the relative speed.Relative speed = 62 km/h - 44 km/h = 18 km/h.Step 2: Convert 18 km/h to m/s.Speed in m/s = 18 * (5/18) = 5 m/s.Step 3: Compute the total effective distance to be covered for overtaking.Total length = 85 m + 75 m = 160 m.Step 4: Use time = distance / speed.Time = 160 m / 5 m/s = 32 seconds.

Verification / Alternative check:
An approximate check confirms the result. At 5 m/s, in 10 seconds the relative distance covered is 50 m, in 20 seconds it is 100 m, and in 30 seconds it is 150 m. To cover 160 m, it should take just a little more than 30 seconds, which matches exactly with 32 seconds from the accurate calculation. Therefore, 32 seconds is consistent and correct.

Why Other Options Are Wrong:
- 22 seconds and 42 seconds would correspond to distances of 110 m and 210 m at 5 m/s, which do not match the 160 m needed.
- 52 seconds would correspond to 260 m at 5 m/s, which is longer than required.
Only 32 seconds is consistent with the correct relative speed and combined length of the trains.

Common Pitfalls:
It is easy to forget to add both train lengths when calculating the overtaking distance. Another frequent error is using the sum of the speeds instead of their difference when the trains move in the same direction. Also, using km/h directly without converting to m/s leads to incorrect time values in seconds. Always handle units and relative speed carefully.

Final Answer:
The faster train will completely cross the slower train in 32 seconds.