A man runs at a constant speed of 20 km/h around a circular garden that has a radius of 350 metres. How much time (in seconds) will he take to complete exactly one full round of the circular garden?

Introduction / Context:
This problem combines circular geometry with time and speed concepts. It requires computing the circumference of a circle and then using the basic speed formula to compute the time needed to cover that circumference. It also tests the ability to handle unit conversions between kilometres per hour and metres per second, which is a common theme in time and distance problems.

Given Data / Assumptions:

Speed of the man = 20 km/h.
Radius of the circular garden = 350 metres.
The man runs along the boundary, so he covers the circumference of the circle.
He runs at a constant speed without stopping.
We need the time taken to complete one full round, expressed in seconds.
Use π ≈ 22 / 7 for practical calculation of circumference.

Concept / Approach:
The distance around a circular path is its circumference, given by circumference = 2 * π * r. After computing the circumference in metres, we convert the runner's speed into metres per second to keep units consistent. Then we use time = distance / speed to find the required time. This structured approach ensures correct handling of both geometry and unit conversions.

Step-by-Step Solution:
Step 1: Compute the circumference of the garden. Radius r = 350 m. Use π = 22 / 7. Step 2: Circumference = 2 * π * r = 2 * (22 / 7) * 350 = 44 * 50 = 2200 metres. Step 3: Convert the man's speed from km/h to m/s. Speed = 20 km/h = 20 * 1000 / 3600 m/s = 20000 / 3600 m/s = 5.555... m/s. Step 4: Use the distance and speed to find time: time = distance / speed = 2200 / (20000 / 3600) seconds. Step 5: Simplify: 2200 * 3600 / 20000 = 2200 * 0.18 = 396 seconds. Step 6: Therefore, the man takes 396 seconds to complete one round of the garden.

Verification / Alternative check:
We can approximate using 5.56 m/s for the speed. Then time ≈ 2200 / 5.56 ≈ 395.7 seconds, which rounds to 396 seconds, matching our exact calculation using fractions. This confirms that the numerical result is consistent with both precise fractional and approximate decimal methods.

Why Other Options Are Wrong:
Times such as 336, 376, 360, or 412 seconds correspond to significantly different speeds for the same distance. For example, 2200 / 336 ≈ 6.55 m/s and 2200 / 412 ≈ 5.34 m/s, which are not equal to the given speed of 20 km/h (approximately 5.56 m/s). Only 396 seconds aligns with the given speed after proper unit conversion and circumference calculation.

Common Pitfalls:
A frequent mistake is using diameter instead of radius in the circumference formula or neglecting to multiply by 2. Another common error is forgetting to convert 20 km/h into m/s and instead using inconsistent units, which leads to incorrect time values. Approximating π too coarsely can also create slight discrepancies. Using π = 22 / 7 and carefully converting units ensures an accurate answer.

Final Answer:
The man will take 396 seconds to complete one round of the garden.