Three copying machines A, B, and C, working together at their respective constant rates, can do a copying job in $2$ hours. B and C, working together at their respective constant rates, can do the same copying job in $4$ hours. How many hours would it take A, working alone at its constant rate, to do the same job?

Correct answer marked below

2 hours

3 hours

4 hours

Correct

5 hours

6 hours

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Comments

NicoAug 9

Thanks, this one was pretty straightforward once I set A's rate as the difference between the combined rates.

SimAug 10

Same here, took me like 30 seconds. Nice confidence booster.

Linn4d ago

Wait, why do we subtract B+C's rate from A+B+C's rate? Can someone explain the setup?

Vageeshajust now

Because A's rate plus B and C's rate equals the total rate. So A alone is just the total minus what B and C do together.

Lamanjust now

Think of it as the combined rate of all three minus the combined rate of the other two.

BayazidJun 23

I got 4 at first by mistake, then realized I flipped the rates. Classic.

RobertJun 30

Been there, rate problems always trip me up with the inverses.

PanshulMay 10

Is this really sub-505? Felt a bit tricky to me with the rate conversions.

AlessandroMay 13

Yeah it's easy once you know the trick but the fraction part can confuse people.

What this question tests

Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.

Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.