In a race, the second place finisher crossed the finish line 2 1/5 minutes behind the second place finisher took 39 2/3 minutes. how long did the winner take?

37 7/15 minutes

Step-by-step explanation:

The winner took 2 1/5 minutes less than the 39 2/3 minutes taken by the second place finisher. That time is ...

... 39 2/3 - 2 1/5 = (39 -2) + (2/3 -1/5) = 37 + (5·2 -3·1)/(3·5)

... = 37 7/15 . . . . minutes

It might be easier to compute the time in minutes and seconds.

... 39 2/3 minutes = 39 minutes 40 seconds

... 2 1/5 minutes = 2 minutes 12 seconds

Then the difference is ...

... (39 -2) minutes (40 -12) seconds = 37 minutes 28 seconds

Adding fractions

The sum of fractions a/b and c/d can be found as ...

... a/b + c/d = (ad +bc)/(bd)

For a=2, b=3, c=-1, d=5, the sum is (2·5+3·(-1))/(3·5) = (10-3)/15 = 7/15

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Time conversions

A minute is 60 seconds, so the number of seconds in a fraction of a minute is found by multiplying that fraction by 60 seconds.

... 2/3 × 60 seconds = 40 seconds

... 1/5 × 60 seconds = 12 seconds

... 7/15 × 60 seconds = 28 seconds

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step-by-step explanati∵∵∴∴on:

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step-by-step explanation: