To cover a distance of 216 km in 3.2 hours, what should be the average speed of the car in metres per second (m/s)?

Introduction / Context:
This question is another straightforward average speed calculation with a twist: the final answer must be in metres per second (m/s). A car must cover 216 km in 3.2 hours, and we are asked what average speed is required. Such problems are common in aptitude tests and require both the correct use of speed = distance / time and the conversion from km/h to m/s.

Given Data / Assumptions:

• Total distance = 216 km.
• Total time = 3.2 hours.
• The car travels with constant average speed.
• We must express this speed in m/s.

Concept / Approach:
First compute the average speed in km/h using:
average speed = distance / time Then convert the result from km/h to m/s using:
1 km/h = 5 / 18 m/s This two-step method keeps the calculation organised and clear.

Step-by-Step Solution:
Step 1: Compute average speed in km/h. Distance = 216 km, time = 3.2 hours. average speed (km/h) = 216 / 3.2. Write 3.2 as 32 / 10. So 216 / 3.2 = 216 / (32 / 10) = 216 * (10 / 32). Simplify 216 / 32: 216 / 32 = 6.75. Then 6.75 * 10 = 67.5 km/h. Step 2: Convert 67.5 km/h to m/s. Speed in m/s = 67.5 * (5 / 18). First compute 67.5 / 18. 67.5 / 18 = 3.75. Now multiply by 5: 3.75 * 5 = 18.75 m/s. Therefore, the required average speed is 18.75 m/s.
Verification / Alternative check:
We can reverse the conversion. Convert 18.75 m/s back to km/h:
speed (km/h) = 18.75 * (18 / 5) = 18.75 * 3.6. 18.75 * 3.6 = 67.5 km/h. Now check if 67.5 km/h for 3.2 hours produces 216 km:
distance = 67.5 * 3.2 = 67.5 * (32 / 10) = (67.5 * 32) / 10. 67.5 * 32 = 2160. 2160 / 10 = 216 km. The distance matches, so our calculations are correct.

Why Other Options Are Wrong:
33.75 m/s corresponds to a much higher km/h value, so the car would cover more than 216 km in 3.2 hours.
37.5 m/s is even faster and clearly too big.
27 m/s and 16.5 m/s correspond to other average speeds that, when converted and multiplied by 3.2 hours, do not give 216 km.
Only 18.75 m/s corresponds exactly to 216 km in 3.2 hours.

Common Pitfalls:
Errors often occur while dividing 216 by 3.2, particularly when handling decimals. Some learners forget to convert km/h to m/s or use the wrong conversion factor. Another mistake is rounding intermediate values too early, which can change the final answer. Keeping fractional calculations exact until the final step and remembering the factor 5 / 18 for km/h to m/s prevents most errors.

Final Answer:
The car must travel at an average speed of 18.75 m/s to cover 216 km in 3.2 hours.