Two goods trains, each 520 m long, are running in opposite directions on parallel tracks at speeds of 42 km/h and 36 km/h respectively. How many seconds will they take to completely cross each other?

Introduction / Context:
This question deals with two trains of equal length running in opposite directions. It checks understanding of how to compute relative speed when trains move towards each other and how to apply the distance equals speed times time relationship when the distance to be covered is the sum of both train lengths.

Given Data / Assumptions:

• Length of each goods train = 520 m.
• Speed of first train = 42 km/h.
• Speed of second train = 36 km/h.
• They move in opposite directions on parallel tracks.
• We want the time for them to completely cross each other.

Concept / Approach:
When two objects move towards each other, the relative speed is the sum of their individual speeds. To cross each other completely, the front of each train must travel past the entire length of the other train, so the total distance involved is the sum of both lengths. Once we convert the relative speed to m/s, we can compute the time as distance divided by relative speed.

Step-by-Step Solution:
Total distance to be covered while crossing = 520 m + 520 m = 1040 m. Relative speed in km/h = 42 + 36 = 78 km/h. Convert relative speed to m/s: 78 * (5 / 18) = 390 / 18 ≈ 21.67 m/s. Time taken to cross each other = distance / relative speed = 1040 / 21.67 ≈ 48 s.

Verification / Alternative check:
We can keep the values exact: 78 km/h = 78 * 5 / 18 = 390 / 18 = 65 / 3 m/s. Then time = 1040 / (65 / 3) = 1040 * 3 / 65 = 3120 / 65 = 48 s exactly. This confirms that 48 seconds is not just an approximation but the exact value based on the given data.

Why Other Options Are Wrong:
Times such as 60 s, 45 s, or 34 s do not correspond to the correct ratio of distance to relative speed. If we multiply these times by the relative speed 65 / 3 m/s, the resulting distances are not equal to 1040 m, so they cannot represent the correct crossing time for the given train lengths.

Common Pitfalls:
Learners sometimes forget to add both train lengths and use only one length, which halves the required distance and gives a wrong time. Another error is to subtract the speeds instead of adding them, which is appropriate only when trains move in the same direction. Additionally, incorrect conversion between km/h and m/s can significantly change the numerical result.

Final Answer:
The two goods trains will completely cross each other in 48 sec.