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

First place finisher finished 31 7/12 minutes or 31 minutes and 35 seconds

Step-by-step explanation:

The question says that In a race, the second place finisher crossed the finish line 1 1/3 minutes after the winner. The third place finisher was 1 3/4 minutes behind the second place finisher. The third place finisher took 34 2/3 minutes how long did the winner take?

Let's assume that the first place finisher finished at X minutes.

And the second place finisher finished at 4/3 minutes after the first place finisher.

The above statement means

X + 4/3 = time of the second place finisher.

And the third place finisher finished 7/4 minutes after the second place finisher and his timing was 104/3 minutes.

This statement with lead to the equation

X + 4/3 + 7/4 = 104/3 minutes.

X = 104/3 - 7/4 - 4/3

X = 31 7/12.

Therefore, the first place finisher finished 31 7/12 minutes or 31 minutes and 35 seconds

Answer: 31 7/12 minutes

Step-by-step explanation:

Hi, if we subtract the time difference between the second and third place to the third place finisher's time (34 2/3 - 13/4), we obtain the second place finisher's time. (Since the third place time is equal to the second place time + the difference between the 2nd and 3rd)

If we subtract the time difference between the first and second place to the second place finisher's time, we obtain the winner's finishing time.

So, we have to subtract both differences to the third place finisher's time, to obtain the winner's finishing time.

34 2/3 - 1 1/3 - 1 3/4 =

33 1/3 - 1 3/4 =

33 4/12 - 1 9/12 =

32 (12/12 + 4/12) - 1 9/12=

32 16/12 - 1 9/12 = 31 7/12 minutes