It takes machine a x hours to manufacture a deck of cards that machine b can manufacture in y hours. if machine a operates alone for z hours and is then joined by machine b until 100 decks are finished, for how long will the two machines operate simultaneously?

The expression that shows how long the two machines will operate simultaneously is:

Step-by-step explanation:

We know that:

x: hours to manufacture a deck of cards for machine A

y: hours to manufacture a deck of cards for machine B

z: hours that machine A operates alone

The number of decks manufactured only by machine A is:

So, the remaining decks are given by:

Then, the combined rate of machines A and B would be:

The work-rate formula is:

Hence, the time that the two machines work simultaneously is:

d.192

step-by-step explanation:

12*16=192

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