Introduction / Context:
This question is another example of trains running in opposite directions. It asks for the time needed for two superfast trains of different lengths to completely cross each other. The problem combines relative speed, the total effective distance, and correct unit handling.
Given Data / Assumptions:
- Length of first train = 140 m.
- Length of second train = 160 m.
- Speed of first train = 60 km/h.
- Speed of second train = 80 km/h.
- They run on parallel tracks in opposite directions.
Concept / Approach:
When two trains run towards each other, the relative speed is the sum of their speeds. The total distance that needs to be covered for each train to completely clear the other is the sum of their lengths. After converting the relative speed into m/s, we can find the crossing time as distance divided by relative speed.
Step-by-Step Solution:
Total distance for complete crossing = 140 m + 160 m = 300 m.
Relative speed in km/h = 60 + 80 = 140 km/h.
Convert to m/s: 140 * (5 / 18) = 700 / 18 ≈ 38.89 m/s.
Time taken to cross each other = distance / relative speed = 300 / 38.89 ≈ 7.71 s.
Verification / Alternative check:
Using exact fractions, 140 km/h = 140 * 5 / 18 = 700 / 18 m/s. Then time = 300 / (700 / 18) = 300 * 18 / 700 = 5400 / 700 = 54 / 7 ≈ 7.714 s. Rounded to two decimal places, this is 7.71 s, which matches the answer option.
Why Other Options Are Wrong:
Times such as 9.36 s, 8.45 s, or 10.48 s would correspond to different effective speeds or distances and do not satisfy the equation time = 300 / (700 / 18). If we multiply any of these times by the relative speed, we do not get a distance of 300 m, so they cannot represent the correct crossing time.
Common Pitfalls:
Mistakes often include subtracting the speeds instead of adding them and forgetting to add the lengths of both trains when calculating the distance. Also, some students mis-handle decimal approximations. Keeping exact fractional values as long as possible helps to avoid rounding errors and identify the correct option.
Final Answer:
The two superfast trains will completely cross each other in approximately
7.71 sec.
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