Here is a non-standard way to look at the work problem:
assign numbers to the "job."
Take this particular question as an example.
Machines X can complete a certain job in 9 hours.
Let the job be: in this case, making 9 pieces of candies
So, Machine X's work rate = 1 candy per hour.
Then the question stated:
Machine X worked on the job alone for the first 3 hours
So, 6 more pieces of candies to go
Next: The two machines, working together, then completed the job in 4 more hours
We know that Machine X can produce 4 pieces of candies in 4 hours
So, Machine Y produces 2 pieces of candies in 4 hours, which is 0.5 piece per hour.
Thus, it will take 18 hours to produce 9 pieces of candies for machine Y alone.
This is what I came up with on the fly during the actual GMAT on a work problem that kinda confused me when I tried with the standard work function way... wondering why I didn't think of this way earlier.....
Nice and easy, with no fraction to confuse you... not to mention that candies are sure yummy
Your East Coast bias is worse than ESPN.