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

Respuesta :

Answer:   31 & 7/12 minutes

This is the same as 31  7/12  minutes

It's a mixed number with

  • whole part = 31
  • fractional part = 7/12

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Explanation

I'll use an ampersand symbol to separate the whole part from the fractional part.

For instance 1  1/3 will be written as 1 & 1/3

Rewrite each mixed number so that the fractional part has the LCD 12 (since 3*4 = 12).

  • 1 & 1/3 = 1 & 4/12
  • 1 & 3/4 = 1 & 9/12
  • 34 & 2/3 = 34 & 8/12

We then subtract the last two values to find how long the 2nd place runner took.

(34 & 8/12) - (1 & 9/12)

(34 + 8/12) - (1 + 9/12)

(33 + 1 + 8/12) - (1 + 9/12)

(33 + 12/12 + 8/12) - (1 + 9/12)

(33 + 20/12) - (1 + 9/12)

33 + 20/12 - 1 - 9/12

(33 - 1) + (20/12 - 9/12)

32 + (11/12)

32 & 11/12

In short,

(34 & 8/12) - (1 & 9/12) = 32 & 11/12

Therefore, the 2nd place runner took 32 & 11/12 minutes. You can use WolframAlpha to confirm.

For the last batch of steps, we subtract (32 & 11/12) and (1 & 4/12) to find the time value of the 1st place runner.

(32 & 11/12) - (1 & 4/12)

(32 + 11/12) - (1 + 4/12)

32 + 11/12 - 1 - 4/12

(32 - 1) + (11/12 - 4/12)

31 + (7/12)

31 & 7/12 which is the final answer

You can write the answer as 31  7/12 if you wanted.