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

4400

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: