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stumped by work flow problem

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stumped by work flow problem

by cookiemonster26 » Thu Dec 11, 2008 8:46 am
Hi Guys,

Was hoping if someone could please help me find the solution to this problem. The question is

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
A 18 days
B 27 days
C 26.67 days
D 16 days
E 12 days

The actual answer is A = 18 days but when i work it out i get 14 days. THis is my reasoning

Formula I used Work = People * rate * time

lets say total number of days required to complete the job = x
so number of days that A and B work together is = x-10
so work done(W1) in these (x-10) days = 2 * (1/20 + 1/30) * (x-10)

After (x-10) days, only B works
SO work done by B(W2) in the 10 remaining days = 1 * (1/30) * 10
= 1/3 rd for total work

Now total work =1
so W1 + W2 = 1

thus if you solve for x you will then get 14 days. but the answer should be 19 days.

What am i doing wrong? Please help!!
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by dendude » Thu Dec 11, 2008 10:11 am
Are you sure the actual answer is 18 days?
I got the answer as 27 days
Here's my reasoning,

A can do 1/20 of the work in 1 day
B can do 1/30 of the work in 1 day

If A and B work together they can finish the work in 12 days

A leaves 10 days before the work is complete
i.e A and B work together only for 2 days

so in 2 days (1/20 + 1/30)*2 = 1/6th of the work is done

B has to complete the remaining 5/6th of the work, which he can do in
30*5/6 = 25 days

Therefore total work gets done in 25 + 2 = 27 days.

Let me know if this makes sense
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by dmateer25 » Thu Dec 11, 2008 10:12 am
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

I am coming up with 18.

Rate of A = 1/20
Rate of B=1/30

We know that B works on the project the entire time and A quits 10 days before finished.

Let d = days b worked on project
d-10 = days a worked on project

The total work completed at will be 1. (1 project)

d/30 + (d-10)/20 = 1

(2d + 3d – 30)/60 = 1

5d – 30 = 60

5d = 90

d =18
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by cramya » Thu Dec 11, 2008 10:18 am
I agree with Dendude on 27 days.

Dmateer,
I see how u r getting 18. How can we say the work gets done in d days(sure I am missing something)?

IMO only 1/6 the of the work gets done working together so to do 5/6 the of the work B may require more than 18 days since it takes 30 days to do 1 job

I am sure one of us is assuming something incorrectly. You may very well be correct.

We will wait on other responses also.

Regards,
Cramya
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by dmateer25 » Thu Dec 11, 2008 10:28 am
Try plugging in the answer choices.

A completes 1/20 in a day
B completes 1/30 in a day


If they work 18 days

A completes 18/20. However, A would only work 8 days because they work 10 less than the total. So the rate would be 8/20
B completes 18/30

8/20 + 18/30

24/60 + 36/60 = 60/60 = 1
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by sanju855 » Thu Dec 11, 2008 10:54 am
A leaves 10 days before the project is finished. So, B works for the last 10 days alone.
In 1 day, B can do 1/30th part of the work.
So, in 10 days, B does 10/30 or 1/3 of the work.
So, the remaining 2/3 of the work is done by A and B together.
In 1 day, A+B can do (1/20+1/30)=1/12th part of the work.
1/12th part of the work is done in 1 day by A+B.
2/3 part of the work will be done in 2/3/1/12=8 days by A+B

So, the whole work will be finished in 10+8=18 days.
Regards,
Sanjoy
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Re: stumped by work flow problem

by parallel_chase » Thu Dec 11, 2008 10:57 am
A's rate = 1/20

B's rate = 1/30

combined A + B rate = 1/12

A quit 10 days before the project ended

Therefore, B works alone for 10 days --------I

1/30 * 10 = 1/3 work completed alone by B

Remaining work left = 1-1/3 = 2/3

2/3 of the project completed by A and B together

Therefore,

2/3 / 1/12 = 8 days ------------II

I + II = 10 + 8 = 18

Hope this helps.
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by cramya » Thu Dec 11, 2008 11:08 am
Guys,
What flaw do u see with Dendude's approach?

parallel chase:

combined A + B rate = 1/12

Agree this means they finish the job in 12 days but A quits 10 days before.

12-10 = 2

A works with B TOGETHER FOR 2 DAYS

In 2 days 1/12*2 = 1/6 the work completed

Remaining 5/6 th wrk B has to do alone which takes him 25 days

25+2 = 27


I must be blanking out as i may be approaching this incorrectly
:?
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by dmateer25 » Thu Dec 11, 2008 11:12 am
cramya wrote:Guys,
What flaw do u see with Dendude's approach?

parallel chase:

combined A + B rate = 1/12

Agree this means they finish the job in 12 days but A quits 10 days before.

12-10 = 2

A works with B TOGETHER FOR 2 DAYS

In 2 days 1/12*2 = 1/6 the work completed

Remaining 5/6 th wrk B has to do alone which takes him 25 days

25+2 = 27


I must be blanking out as i may be approaching this incorrectly
:?

I think you are reading the question incorrect. It says A quits 10 days before the job is complete.

Your approach would be correct if it said A quit 10 days before the time it takes A and B working together to complete the job.
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by parallel_chase » Thu Dec 11, 2008 11:17 am
cramya wrote:Guys,
What flaw do u see with Dendude's approach?

parallel chase:

combined A + B rate = 1/12

Agree this means they finish the job in 12 days but A quits 10 days before.

12-10 = 2

A works with B TOGETHER FOR 2 DAYS

In 2 days 1/12*2 = 1/6 the work completed

Remaining 5/6 th wrk B has to do alone which takes him 25 days

25+2 = 27


I must be blanking out as i may be approaching this incorrectly
:?

dude you are not blanking out, I got 27 as the answer initially. But I dont think this can be a real GMAT question, otherwise question must have mention some details about who is working alone. May be C came in and helped B. :)

I agree with Dmateer's reasoning but again the question is ambiguous, which we all know that it cant be the case on real GMAT or GMAT prep. So, sincere suggestion forget about it. Like I just did :D

If you still want to take a shot at it, calculate it with the flow of the question. A quit 10 days before the project was completed.
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by adilka » Thu Dec 11, 2008 11:22 am
cramya wrote:Guys,
What flaw do u see with Dendude's approach?

parallel chase:

combined A + B rate = 1/12

Agree this means they finish the job in 12 days but A quits 10 days before.

12-10 = 2

A works with B TOGETHER FOR 2 DAYS

In 2 days 1/12*2 = 1/6 the work completed

Remaining 5/6 th wrk B has to do alone which takes him 25 days

25+2 = 27


I must be blanking out as i may be approaching this incorrectly
:?


You are not comparing apples to apples here by subtracting 10 from 12.
A quits 10 days before the total job is complete (party by A&B and partly by B) , not 10 days before what it would've taken A&B to complete the job together.
In other words, to apply your logic you should be substracting 10 fom 18, not from 12 (you don't know that 18 is 18 until you solve for it)

I know it's a but convoluted.
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by cookiemonster26 » Thu Dec 11, 2008 12:01 pm
so guys..whats the answer then?

can you please have a look at the procedure I followed(the first post) and tell me what it is that I did wrong?

Thanks a bunch.
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Re: stumped by work flow problem

by adilka » Thu Dec 11, 2008 12:22 pm
Your mistake is in the following operation:
cookiemonster26 wrote: so work done(W1) in these (x-10) days = 2 * (1/20 + 1/30) * (x-10)
Why are you multiplying by 2? You are already adding the rates of A and B (1/20 + 1/30), so this is a combined rate at which the work was being done for x-10 days. Then the job was being done for 10 days at 1/30.

You do not need to multiply by 2. Not sure what your reasoning was behind this 2 factor.
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by Stuart@KaplanGMAT » Thu Dec 11, 2008 12:26 pm
cookiemonster26 wrote:so guys..whats the answer then?

can you please have a look at the procedure I followed(the first post) and tell me what it is that I did wrong?

Thanks a bunch.
Your methodology is great. The problem lies with your application of the work formula:

Work = People * rate * time

You applied the formula as:

W1 = 2 * (1/20 + 1/30) * (x-10)

In doing so, you double counted the work done. (1/20 + 1/30) already accounts for the work of BOTH A and B. By also multiplying by 2, you've overcompensated. You only multiply by the number of workers if each one works at the same rate.

Removing the extra factor of 2:

2/3 = (1/20 + 1/30) * (x-10)

2/3 = (3/60 + 2/60) * (x-10)

2/3 = 5/60 * (x-10)

2/3 = 1/12 * (x-10)

(2/3)(12/1) = x - 10

24/3 = x - 10

8 = x - 10

18 = x

Giving us the correct answer to the question.
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by cookiemonster26 » Thu Dec 11, 2008 12:41 pm
Thanks a bunch Stuart.

You rock...
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