Machines operating simultaneously

alivapriyada wrote: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

alivapriyada wrote: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

diebeatsthegmat wrote:

alivapriyada wrote: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