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# The Quest for 700: Weekly GMAT Challenge (Answer)

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 ac. 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:

ac = 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.

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