Question

In a race, the second place finisher crossed the finish line minutes after the winner. The third-place1 1 3 finisher was minutes behind the second placefinisher. The third place finisher took minutes. How1 3 4 34 2 3 long did the winner take?

Answer 1

To find the winning time in the race, we subtract the time differences between the placements from the total time of the third-place finisher. The winner took 32 minutes to complete the race.

Step-by-step explanation:

The student is asking about the time taken by the winner of a race given the times for the third-place and second-place finishers. To solve the problem, we need to subtract the time differences between the first and second, and the second and third finishers, from the total time taken by the third-place finisher.

Let's denote:

• Tw as the winner's time,
• Ts as the second-place finisher's time,
• Tt as the third-place finisher's time.

According to the problem:

• Ts = Tw + 1 1/3 minutes,
• Tt = Ts + 1 1/3 minutes,
• Tt = 34 2/3 minutes.

To find the winner's time Tw:

1. First, we find the second-place time:
   Ts = Tt - 1 1/3 minutes
   Ts = 34 2/3 minutes - 1 1/3 minutes
   Ts = 33 1/3 minutes
2. Then we find the winner's time:
   Tw = Ts - 1 1/3 minutes
   Tw = 33 1/3 minutes - 1 1/3 minutes
   Tw = 32 minutes

Hence, the winner took 32 minutes to finish the race.