Final answer:
To find the winner's time in the race, first determine the second-place finisher's time by subtracting 1 3/4 minutes from the third-place finisher's time, and then find the winner's time by subtracting 1 1/3 minutes from the second-place time, yielding a time of 31 7/12 minutes for the winner.
Step-by-step explanation:
Step-by-Step Solution to Time Calculation in a Race
The question involves a race in which the time intervals between the finishers are given. The goal is to determine the time taken by the winner of the race. To do this, we use the information about the third-place finisher and calculate backwards from there.
The third-place finisher completed the race in 34 2/3 minutes. We know that the third-place finisher was 1 3/4 minutes behind the second-place finisher. Therefore, the time taken by the second-place finisher can be calculated as:
Time of third-place finisher - Time behind second-place = Time of second-place finisher
34 2/3 minutes - 1 3/4 minutes = 34 2/3 minutes - 7/4 minutes
Converting 34 2/3 minutes to fraction: 34 + 2/3 = (34×3 + 2) / 3 = (102 + 2) / 3 = 104/3 minutes
Now we subtract 7/4 minutes from 104/3 minutes:
(104/3) - (7/4) = (416 - 21) / 12 = 395 / 12 minutes
395/12 minutes simplifies to 32 11/12 minutes.
Now, we calculate the time taken by the winner. The second-place finisher crossed the finish line 1 1/3 minutes after the winner. So we subtract this time from the second-place finisher's time to find the winner's time:
32 11/12 minutes - 1 1/3 minutes
We convert 1 1/3 minutes to fractions: 1 + 1/3 = (1×3 + 1) / 3 = (3 + 1) / 3 = 4/3 minutes
Now we subtract 4/3 minutes from 32 11/12 minutes:
(395/12) - (4/3) = (395 - 16) / 12 = 379 / 12 minutes
The winner's time is thus 31 7/12 minutes.
The RDW (Read-Draw-Write) strategy is applied by first reading and understanding the problem, then drawing a representation if necessary, and finally writing out the solution step by step, as shown in this explanation.