It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?
100y – x
--------------
x2 + 1
100x – y
--------------
x2 + 1
100y – x3 – x
------------------
x2 + 1
100y – x2y – y
---------------------
x2 + 1
100x
------------
x2 + 1
100y – x
--------------
x2 + 1
100x – y
--------------
x2 + 1
100y – x3 – x
------------------
x2 + 1
100y – x2y – y
---------------------
x2 + 1
100x
------------
x2 + 1
