A boy runs around a square field with side length 35 metres at a constant speed of 9 km/h. How much time in seconds will he take to complete one full round of the field?

Introduction / Context: This question combines basic perimeter calculation of a square with unit conversion from km/h to m/s or metres per second. It is a common type of problem in time and distance topics that checks both geometry and speed conversion skills. Given Data / Assumptions:

• Shape of field: square.
• Side length of the square field = 35 metres.
• Running speed of the boy = 9 km/h.
• We must find the time taken to complete one full round (one perimeter) in seconds.

Concept / Approach: First, we compute the perimeter of the square, which is 4 times the side. Then we convert the speed from km/h to m/s or interpret distance and speed consistently. Time is always given by: Time = Distance / Speed. It is often convenient to express speed in metres per second when distance is in metres and time is required in seconds. Step-by-Step Solution: Step 1: Perimeter of the square = 4 * side = 4 * 35 = 140 metres. Step 2: Convert speed from km/h to m/s. Use 1 km/h = 5 / 18 m/s. Step 3: Speed = 9 km/h = 9 * 5 / 18 m/s = 45 / 18 m/s = 2.5 m/s. Step 4: Time taken = Distance / Speed = 140 / 2.5 seconds. Step 5: 140 / 2.5 = 56 seconds. Verification / Alternative check: Instead of converting into metres per second, we could convert distance into kilometres and time into hours. Distance = 140 metres = 0.14 km. Time in hours = 0.14 / 9 hour, and then convert that to seconds: Time in hours = 0.015555..., multiply by 3600 seconds per hour gives 56 seconds, again confirming the result. Why Other Options Are Wrong:

• 50 seconds: Corresponds to a slightly higher speed than 9 km/h.
• 52 seconds: Also implies a speed greater than the given 9 km/h.
• 54 seconds: Represents a small calculation error when dividing 140 by 2.5.

Common Pitfalls:

• Using side instead of perimeter, forgetting that the boy runs around all four sides.
• Incorrectly converting 9 km/h to m/s by using 18/5 instead of 5/18.
• Mixing units by using metres for distance and km/h for speed without conversion.

Final Answer: The boy will take 56 seconds to complete one round of the square field.