Hi All,
This question can be solved in a couple of different ways (and they all require a certain amount of 'math work', so this question will likely take you at least 2-3 minutes to solve it regardless of how you approach it).
Here's a way to approach it that involves rates and TESTing VALUES.
We're told that it takes Machines A and B, working together, to fill the bin in 6 minutes. Conceptually, it's easiest if those 2 Machines have the same rate, so let's TEST:
Machine A = 12 minutes to fill the bin alone
Machine B = 12 minutes to fill the bin alone
Thus, in 6 minutes, each of them will fill half the bin.
Next, we're told that it takes Machines B and C, working together, to fill the bin in 9 minutes. Since we've set Machine B's rate, we have to mathematically determine Machine C's rate.
In 9 minutes, Machine B will fill 3/4 of the bin. Thus, in those 9 minutes, Machine C has to fill the other 1/4 of the bin.
9 minutes = (1/4)(Full)
36 minutes = Full
Machine C = 36 minutes to fill the bin alone
Now that we've established the rates for Machines A and C, we can calculate how long it takes to fill the bin when Machine A is FILLING the bin and Machine C is EMPTYING the bin.
In 1 minute, Machine A 'fills' 1/12 of the bin. In that same minute, Machine C 'empties' 1/36 of the bin...
1/12 - 1/36 =
3/36 - 1/36 =
2/36
1/18
Thus, every minute, 1/18 of the bin is filled. Knowing that, it takes 18 minutes to fill the bin under these conditions.
Final Answer:
GMAT assassins aren't born, they're made,
Rich