Machines operating simultaneously

[alivapriyada]

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?


A. (100xy - z)/(x + y)

B. y(100x - z) /(x + y)

C. 100y(x - z)/(x + y)

D. x + y /(100xy - z)

E. (x + y - z)/ 100xy

[goyalsau]

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?


A. (100xy - z)/(x + y)

B. y(100x - z) /(x + y)

C. 100y(x - z)/(x + y)

D. x + y /(100xy - z)

E. (x + y - z)/ 100xy

I will go with B.
what's the answer?

[diebeatsthegmat]

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?


A. (100xy - z)/(x + y)

B. y(100x - z) /(x + y)

C. 100y(x - z)/(x + y)

D. x + y /(100xy - z)

E. (x + y - z)/ 100xy

A made 1 deck of card in x hour so in x hour it will make z/x deck of card
then B join with A.
the time it takes both A and B to make a deck of card is 1/x+1/y=1/a ( a is the time) so a= xy/x+y)
thus together they both have to make 100-z/x in b hour
b=(100-z/x)*xy/(x+y)
you calculated that and get the right answer B

[alivapriyada]

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?


A. (100xy - z)/(x + y)

B. y(100x - z) /(x + y)

C. 100y(x - z)/(x + y)

D. x + y /(100xy - z)

E. (x + y - z)/ 100xy

A made 1 deck of card in x hour so in x hour it will make z/x deck of card
then B join with A.
the time it takes both A and B to make a deck of card is 1/x+1/y=1/a ( a is the time) so a= xy/x+y)
thus together they both have to make 100-z/x in b hour
b=(100-z/x)*xy/(x+y)
you calculated that and get the right answer B

many thanks!!! answer is B