A bus covers a distance of 720 kilometres in 20 hours while travelling at a constant speed. Using the basic speed formula and appropriate unit conversion, what is its average speed expressed in metres per second?

Introduction / Context:
This question assesses the understanding of average speed and unit conversion from kilometres per hour to metres per second. It is a standard numerical problem that strengthens the relationship between distance, time, and speed, and is particularly relevant for exams that require quick mental calculations with unit conversions.

Given Data / Assumptions:

Total distance travelled by the bus = 720 kilometres.
Total time taken = 20 hours.
The speed is assumed constant during the entire journey.
We need to express the final answer in metres per second.
Use 1 kilometre = 1000 metres and 1 hour = 3600 seconds as standard conversion factors.

Concept / Approach:
The formula for average speed is speed = distance / time. We first calculate the speed in kilometres per hour by dividing 720 by 20. After that, we convert the speed to metres per second using the standard relation between km/h and m/s. Specifically, to convert km/h to m/s, we multiply by 1000 and then divide by 3600, which is equivalent to dividing by 3.6. This results in the speed expressed in the desired unit.

Step-by-Step Solution:
Step 1: Compute the speed in km/h: speed_kmph = 720 / 20 = 36 km/h. Step 2: Use the relation 1 km/h = 1000 metres / 3600 seconds = 1 / 3.6 m/s. Step 3: Convert 36 km/h into m/s: speed_mps = 36 / 3.6. Step 4: Evaluate 36 / 3.6 = 10, so the bus moves at 10 metres per second on average. Step 5: Therefore, the average speed of the bus is 10 m/s.

Verification / Alternative check:
We can cross check by converting the total distance and time directly into metres and seconds. Distance = 720 kilometres = 720 * 1000 = 720000 metres. Time = 20 hours = 20 * 3600 = 72000 seconds. Hence, speed = 720000 / 72000 = 10 metres per second. This independent computation confirms that the calculated value is correct.

Why Other Options Are Wrong:
Values such as 12, 15, 18, or 20 m/s correspond to significantly different combinations of distance and time and are inconsistent with 720 kilometres in 20 hours. For example, 12 m/s would give a distance of 12 * 72000 = 864000 metres, which is 864 kilometres, not 720 kilometres. Only 10 m/s reproduces the exact given journey details.

Common Pitfalls:
Common mistakes include forgetting to divide by 3.6 when converting from km/h to m/s or incorrectly multiplying instead. Some learners also miscalculate 36 / 3.6 or treat 720 / 20 as 20 instead of 36. Carefully applying the formula speed = distance / time and paying attention to unit conversion steps prevents such errors.

Final Answer:
The average speed of the bus is 10 metres per second.