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Machines A, B, and C can either load nails into a bin or [#permalink]
29 Oct 2009, 18:01

Expert's post

00:00

A

B

C

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Difficulty:

25% (medium)

Question Stats:

83% (02:42) correct
17% (02:57) wrong based on 198 sessions

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?

A - C= 5.55% That means A's loading and C's unloading together complete 5.55% of work in a minute.

100% of work will take 18 mins (100/5.55).

PS - I have been solving all Work Rate problems in this forum since morning with percentage approach and I found each one of them quite simple to solve using percentages. I don't have time else I would have submitted solutions for each problem.

A - C= 5.55% That means A's loading and C's unloading together complete 5.55% of work in a minute.

100% of work will take 18 mins (100/5.55).

PS - I have been solving all Work Rate problems in this forum since morning with percentage approach and I found each one of them quite simple to solve using percentages. I don't have time else I would have submitted solutions for each problem.

_________

Ravender Pal Singh

You dont really have to convert fractions into percentages as it can be extremely time consuming.

A - C= 5.55% That means A's loading and C's unloading together complete 5.55% of work in a minute.

100% of work will take 18 mins (100/5.55).

PS - I have been solving all Work Rate problems in this forum since morning with percentage approach and I found each one of them quite simple to solve using percentages. I don't have time else I would have submitted solutions for each problem.

_________

Ravender Pal Singh

You dont really have to convert fractions into percentages as it can be extremely time consuming.

I have just given detailed explanation for your understanding. There is no sense in calculating 100/5.55 as it is pretty obvious that it would be slightly less than 20 (range in between 16.66 - 20). The best thing about GMAT is that one need not do the complete calculation to solve the question. Once you get the equation, one can easily guess the answer as GMAT has answer options in a good range. Instead of having equations in inverted ratios, if we can have linear equations at one go, solution becomes very simple to correctly guess. I have solved so many questions till now and none of them took more than 1-2 mins.

Re: Machines A, B, and C can either load nails into a bin or [#permalink]
15 Nov 2012, 22:52

\frac{1}{A}+\frac{1}{B}=\frac{1}{T}

It takes A units of time for A to do it alone. It takes B units of time for B to do it alonge. BUT this means it takes T units of time for A and B to accomplish the work where A>T and B>T.

My Solution: \frac{1}{Amin}+\frac{1}{Bmin}=\frac{1}{6min} \frac{1}{Bmin}+\frac{1}{Cmin}=\frac{1}{9min}

Combine the two equations: \frac{1}{Amin}+\frac{1}{Bmin}-\frac{1}{Bmin}-\frac{1}{Cmin}=\frac{1}{6}-\frac{1}{9}

\frac{1}{Amin}-\frac{1}{Cmin}=1/18min

This means A would do 18 minutes of loading while C would do 18 minutes of unloading to complete the task.

Re: Machines A, B, and C can either load nails into a bin or [#permalink]
25 Sep 2013, 20:25

This took a lot of time.

We can use RTW chart, rate * time = work

Combined rate of A/B => 1/A + 1/B = (A+B)/AB

Rate * time = Work

(A+B)/AB * tab = 1 => tab = AB/(A+B) = 6

Getting A in terms of B => A = 6B/(B-6) ..... (1)

Similarly BC/(B+C) = 9

Getting C in terms of B

C = 9B/(B-9)..... (2)

A is loading and C is unloading hence

1/A - 1/C => tac = AC/(C-A)

Substituting values from (1) and (2) we get 18 _________________

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