Find Number of Minutes

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?

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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?

 

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.

 

Nicely-done.