The Correct Answer and Explanation is:
The correct answer is 3.98.
The problem requires selecting the most logical time for the third quarter checkpoint, given that the average time to the finish line is 4.92 seconds. To solve this, we can use a logical approach based on proportional timing.
The finish line represents the completion of the entire race, which can be thought of as four quarters (4/4). The third quarter checkpoint, as its name implies, marks the point where three-quarters (3/4) of the race has been completed. Assuming a relatively consistent pace, the time taken to reach this checkpoint should be approximately three-quarters of the total time.
We can calculate this estimated time by taking 75% of the total finish time. The calculation is as follows:
Total time to finish = 4.92 seconds
Estimated time to third quarter checkpoint = (3/4) * 4.92 seconds
Estimated time = 0.75 * 4.92 = 3.69 seconds
This calculated value of 3.69 seconds serves as a benchmark for what the answer should be if the pace were perfectly even throughout the race. Now, we must compare this estimate to the given options: 3.16, 3.98, and 4.11.
By comparing the options to our estimate:
- The difference between 3.98 and 3.69 is 0.29.
- The difference between 4.11 and 3.69 is 0.42.
- The difference between 3.16 and 3.69 is 0.53.
The option 3.98 is the closest value to our calculated estimate of 3.69 seconds. In real-world events, pace is rarely perfectly constant. A time of 3.98 seconds is very plausible, suggesting a pace that was slightly slower in the initial stages before a final push. The other options are less likely as they would imply a much more drastic and less probable change in pace during the final quarter of the event. Therefore, 3.98 seconds is the most logical choice.
