A train is running at a uniform speed of 116 km/hr. What distance in metres will the train cover in 18 seconds at this speed?

Introduction / Context:
This problem is a straightforward distance calculation given a constant speed and a short time interval. You must convert the train's speed from km/hr to m/s, then use the basic formula distance = speed * time to find how many metres are covered in 18 seconds.

Given Data / Assumptions:
- Speed of the train = 116 km/hr.
- Time interval considered = 18 seconds.
- The train's speed remains constant throughout these 18 seconds.
- We must report the distance in metres.

Concept / Approach:
Since the speed is in km/hr and time is in seconds, we must convert speed into metres per second. The standard conversion is: 1 km/hr = 5 / 18 m/s. After converting, we simply multiply speed (in m/s) by time (in seconds) to get distance in metres.

Step-by-Step Solution:
Step 1: Convert 116 km/hr to m/s using the factor 5 / 18.Step 2: Speed in m/s = 116 * (5 / 18) = 580 / 18 = 290 / 9 m/s.Step 3: The given time is 18 seconds.Step 4: Use distance = speed * time: distance = (290 / 9) * 18 metres.Step 5: Simplify: (290 / 9) * 18 = 290 * 2 = 580 metres.Step 6: Therefore, the train covers 580 m in 18 seconds at 116 km/hr.

Verification / Alternative check:
We can check using approximate values. 116 km/hr is close to 120 km/hr, which is about 33.33 m/s. Our converted speed 290 / 9 is about 32.22 m/s, which is close. At about 32 m/s for 18 seconds, the train would cover around 576 m, which is very close to the exact 580 m. The exact arithmetic confirms 580 m as the correct distance.

Why Other Options Are Wrong:
900 m or 1160 m would require significantly higher speeds or longer times than given. 508 m and 720 m do not correspond to the product of (290 / 9) m/s and 18 seconds. Only 580 m results from a correct conversion and multiplication.

Common Pitfalls:
Students sometimes mistakenly convert the time from seconds to hours and then try to use km/hr directly, which can lead to unnecessary complexity and errors. Another common error is in the km/hr to m/s conversion, such as multiplying by 18 / 5 instead of 5 / 18. Keeping the conversion factor straight and using the simple distance = speed * time formula makes this question easy.

Final Answer:
The train will cover 580 m in 18 seconds at a speed of 116 km/hr.