A train is moving at a speed of 72 km/h. How many seconds will it take to cover a distance of 1400 m?

Introduction / Context:
This is a straightforward speed, distance, and time question often seen in aptitude tests. It involves a train moving at a given speed, and we must determine how long it takes to cover a specified distance, with all units converted consistently.

Given Data / Assumptions:

• Speed of train = 72 km/h.
• Distance to be covered = 1400 m.
• The train moves in a straight line with constant speed.
• We need the time in seconds.

Concept / Approach:
We use the fundamental formula time = distance / speed. Since the distance is given in metres and the answer is required in seconds, it is simplest to convert the speed to metres per second. Once the speed is in m/s, dividing distance in metres by speed immediately gives time in seconds.

Step-by-Step Solution:
Step 1: Convert speed from km/h to m/s using 1 km/h = 5/18 m/s. Step 2: Speed in m/s = 72 * 5 / 18 = 20 m/s. Step 3: Distance to be covered = 1400 m. Step 4: Use time = distance / speed, so time = 1400 / 20 seconds. Step 5: Compute 1400 / 20 = 70 seconds.

Verification / Alternative check:
For a quick check, note that at 20 m/s the train covers 200 m in 10 seconds. Scaling, 1400 m is 7 times 200 m, so the time is 7 times 10 seconds, which is 70 seconds. This mental check confirms the calculation without further algebra.

Why Other Options Are Wrong:

• 80 seconds: This would correspond to an effective speed of 17.5 m/s, not 20 m/s.
• 72 seconds: This would imply a non exact match between the actual speed and the required distance.
• 84 seconds: This is even longer and clearly does not match the value computed using the correct formula.

Common Pitfalls:
Common errors include using distance in kilometres with speed in metres per second or forgetting to convert units at all. Some learners wrongly apply the conversion factor 18/5 instead of 5/18 when changing from km/h to m/s. Always remember that 1 km/h equals 5/18 m/s and not the reverse.

Final Answer:
The train will take 70 seconds to cover 1400 m.