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Two consultants can type up a report in 12.5 hours and edit [#permalink]

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16 Jan 2012, 10:01

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Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

The BIG idea to keep in mind: when two people are working together, what you add are the rates. You never add or subtract the times it takes to work. You add rates.

The question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

I'm going to use the notation: Rmt = the rate at which Mary types Rme = the rate at which Mary edits Rjt = the rate at which Jim types Rje = the rate at which Jim edits Rct = the combined typing rate Rtt = the combined editing rate

The first two numbers tell us about combined rates. If they type a report together in 12.5 = 25/2 hr, then their combined typing rate is Rtt = (1 report)/(25/2 hr) = 2/25. If they edit a report together in 7.5 = 15/2 hr, then their combined editing rate is Rte = (1 report)/(15/2 hr) = 2/15.

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

41.4 34.1 13.4 12.4 10.8

I think this one is pretty hard, can someone please help me with it

Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report" --> Mary's typing rate = 1/30 (rate reciprocal of time) (point 1 in theory below); "Mary and Jim can type up a report in 12.5" and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone) (point 2&3 in theory below)--> x=150/7;

"Jim needs 12 hours to edit the report" --> Jim's editing rate = 1/12; "Mary and Jim can edit a report in 7.5" and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done" --> x+y=150/7+20=~41.4

Answer: A.

THEORY There are several important things you should know to solve work problems:

1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

\(time*speed=distance\) <--> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) --> \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) --> so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) --> so rate of 1 printer is \(rate=2\) pages per hour;

So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).

2. We can sum the rates.

If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together.

3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.

For example if: Time needed for A to complete the job is A hours; Time needed for B to complete the job is B hours; Time needed for C to complete the job is C hours; ... Time needed for N to complete the job is N hours;

Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

41.4 34.1 13.4 12.4 10.8

I think this one is pretty hard, can someone please help me with it

Yes it is a tricky one but you can use some logic to arrive at the answer quickly. The explanation I will write down will be long but when you do it in your head, it will take less than a minute, I promise.

Total time taken to type the report = 12.5 hrs Time taken by Mary alone = 30 hrs Time taken by Jim alone? Let's see. If Jim were to take 30 hrs alone too, together they would have taken 15 hrs. But together they took only 12.5 hrs. My guess is that Jim takes close to 20 hrs alone. Let's see: 1/30 + 1/20 = 5/60 Time taken together = 60/5 = 12 hrs. Close! It means Jim takes a little more than 20 hrs and I would take it as 21 and move on.

Total time taken to edit the report = 7.5 hrs Time taken by Jim alone = 12 hrs Time taken by Mary alone? Now, if Mary were to take 12 hrs too, they could have edited it together in 6 hrs. But they took 7.5 hrs together. So Mary must take more than 12 hrs to edit it alone. I would guess 20 again. Let's see: 1/12 + 1/20 = 8/60 Time taken together = 60/8 = 7.5 hrs - Exactly! So Jim alone takes 21 hrs (apprx) to type it and Mary alone takes 20 hrs to edit it. Together they take 21+20 = 41 hrs (apprx) Answer (A)
_________________

By the way, I have assumed that you will understand some things (e.g. if two people working alone take 30 hrs each, together they will take 15 hrs) since you got a Q42 in your last GMAT. If you need an explanation of these, let me know.
_________________

Two consultants can type up a report in [#permalink]

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23 Jan 2012, 14:29

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

41.4 34.1 13.4 12.4 10.8

does anyone please care to explain. i am having a problem solving this problem
_________________

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

41.4 34.1 13.4 12.4 10.8

does anyone please care to explain. i am having a problem solving this problem

Merging similar questions. manalq8 you are posting the same question the second time, please ask if anything in above explanations was unclear.
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Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]

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26 Nov 2013, 02:49

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Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]

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27 Apr 2015, 06:30

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Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]

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14 May 2015, 02:57

mikemcgarry wrote:

Hi there. I'm happy to help with this.

The BIG idea to keep in mind: when two people are working together, what you add are the rates. You never add or subtract the times it takes to work. You add rates.

The question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

I'm going to use the notation: Rmt = the rate at which Mary types Rme = the rate at which Mary edits Rjt = the rate at which Jim types Rje = the rate at which Jim edits Rct = the combined typing rate Rtt = the combined editing rate

The first two numbers tell us about combined rates. If they type a report together in 12.5 = 25/2 hr, then their combined typing rate is Rtt = (1 report)/(25/2 hr) = 2/25. If they edit a report together in 7.5 = 15/2 hr, then their combined editing rate is Rte = (1 report)/(15/2 hr) = 2/15.

Mary's editing rate is 1/20, so she edits one report in a time of 20 hr.

So, the total time = (21 & change) hours for Jim to type + 20 hrs for Mary to edit = 41 and change hours

That's closest to answer choice A.

I'm sorry, but I disagree with what you posted as the OA. Is it possible that you miscopied?

Does my work here make sense? Please let me know if you have any questions on what I've said here.

Mike

Seriously, how to solve such a question in 2 minutes. It already takes 1 minute to put everything together or even more than one minute ...
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Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]

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02 Jun 2016, 12:10

Hello from the GMAT Club BumpBot!

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