Final answer:
The time of the first-place finisher in the road race is 17.68 minutes, calculated by subtracting the combined times of the other three finishers from the total time for the top four finishers.
Step-by-step explanation:
The problem presented involves finding the time of the first-place finisher given the average running time of the top four finishers and the times of the second, third, and fourth-place finishers. First, we multiply the average time by four to find the total time for all four runners. Then, we subtract the times of the three known finishers from this total. The result will be the time of the first-place finisher.
To solve: Average running time of top 4 finishers × 4 = Total time for top 4 finishers
18.80 min × 4 = 75.2 min
Total time for top 4 finishers - Sum of the times of second-, third-, and fourth-place finishers = Time of the first-place finisher
75.2 min - (18.45 min + 19.27 min + 19.80 min) = First-place finisher's time
75.2 min - 57.52 min = 17.68 min
Therefore, the time of the first-place finisher is 17.68 minutes.