Yesterday, Manhattan GMAT posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
Write each machine’s rate as a lowercase letter. We add the rates for each given situation in which machines are working together to load the bin:
a + b = 1/6 bin per minute
b + c = 1/9 bin per minute
Notice that the rate should always be in “work per time” – in this case, “bins per minute,” not “minutes per bin.” If it takes machines A and B 6 minutes to load the bin, then they work at a rate of 1/6 of a bin per minute.
We are looking for an equation involving the difference of machine A’s rate and machine C’s rate. In other words, we are looking for a – c. The negative sign in front of the c indicates that machine C is unloading; in other words, it is working “against” machine A.
We can subtract the two given equations to get the following:
a – c = 1/6 – 1/9 = 3/18 – 2/18 = 1/18 bin per minute
Thus, it will take 18 minutes for machine A to load the bin, if machine C is simultaneously unloading the bin.
The correct answer is (C).