Hey dumluck,

One suggestion here - because you know that they're giving you a rate (how much can be produced in how much time), you can stay pretty organized by putting everything into the form R = D/T. Which I like because you don't have to memorize it - just think of a rate (miles per hour probably comes to mind - and that's a distance over a time) and the "formula" should come naturally.

So here, Rate of Machine X = twice the number of bottles / 4 hours

or, mathematically: R(x) = 2b / 4

And Rate of Machine Y = the number of bottles / 3 hours

or, mathematically: R(y) = b / 3


The question will have to provide you with more information (e.g. "if, combined, they produce 100 bottles in 5 hours...) or a question stem that asks you for something specific (e.g. "if each works 10 hours, what percent greater will the output of machine x be than machine y). So you can then use that information, similarly, to whittle down the number of variables and solve for what you need to.