Find Number of Minutes

Discussion in 'Algebra' started by nycmathguy, Jun 28, 2021.

  1. nycmathguy

    nycmathguy

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    Selma's class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already boxed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already boxed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?

    Someone here responded by saying this:

    The key to this is to determine the number of boxes they will both have made. Call this N, so that Selma must make N - 12 more and Trudy N - 18.This will take 5(N -12) minutes for Selma and 7(N-18) for Trudy. You find N from the fact that these are equal. Hence N = 33, and so Selma needs 21 more and Trudy 15. As you say, this takes each of them 105 minutes.

    Mira:

    What information in the problem led to N - 12 and N - 18?
     
    nycmathguy, Jun 28, 2021
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  2. nycmathguy

    MathLover1

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    Selma's class is making care packages to give to victims of a natural disaster.

    Selma packs one box in 5 minutes

    Selma’s rate x/5
    and has already boxed 12 boxes

    x/5+12

    Her friend Trudy packs one box in 7 minutes

    x/7
    and has already boxed 18 boxes

    x/7+18

    How many more minutes does each need to work in order to have packed the same number of boxes?

    12 + x/5 = 18 + x/7 (x = amount of time, in minutes)

    x/5 - x/7 = 18 - 12

    (7x)/35 - (5x)/35 = 6

    (2x)/35 = 6

    2x = 35*6

    x= 35*3

    x= 105 minutes or 1 hour and 45 minutes


    Another solution using fingers:
    Every 35 minutes Selma packs 7 boxes, while Trudy packs 5 boxes.
    Thus every 35 minutes Selma decreases the difference between them in 2 boxes.
    Since the original difference was 6 boxes, Selma needs 3 times 35 minutes, or 105 minutes, in all, to catch Trudy.
     
    MathLover1, Jun 28, 2021
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  3. nycmathguy

    nycmathguy

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    Nicely-done.
     
    nycmathguy, Jun 28, 2021
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