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D01-28

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Bunuel
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D01-28 [#permalink] New post   16 Sep 2014, 00:12
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71% (02:39) correct 29% (03:25) wrong based on 220 sessions
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Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?

A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
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C
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Bunuel
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Re D01-28 [#permalink] New post   16 Sep 2014, 00:12
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Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?

A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)


After 2 hours, A, working alone, completes \(2*\frac{1}{10}=\frac{1}{5}\) of the task;

After 4 hours, a total of \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task is completed, with A and B working together for the last 2 hours, leaving \(\frac{1}{5}\) of the task remaining;

We know that the final \(\frac{1}{5}\) of the task is completed in 15 minutes (or \(\frac{1}{4}\) of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From this equation, we can determine that \(x=2\) hours.


Answer: C
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Re: D01-28 [#permalink] New post   30 Aug 2018, 22:15
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A - 10 hours to complete the work
B- 5 hours to complete the work
C- X hours to complete the work
Take the LCM of 10,5,x = 10x (total work)
Hence A rate of work = 10x/10 = X units/hour
B rate of work = 10x/5 = 2x units/hour
C rate of work = 10x/x = 10 units/hour
therefore
X*2 +(2x+x)*2+(2x+x+10)*1/4 =10x
this gives X =2 (quick and easy)
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Re: D01-28 [#permalink] New post   31 Oct 2015, 21:04
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A works alone for 2 hours,
0.2x(work) completed

joins B
0.2x completed by worker A
1/5 => 2/5 completed or 0.4x completed by worker B

after 4 hours we have 0.8x completed
joins C and everything is finished in 15 minutes
or 0.2x (work) is completed in 0.25 hours

now we can set an equation
1/10 + 1/5+ 1/x = 2/10 * 4/1 simplify 1/5 or 4/5
multiply everyting by 10
1+2+10/x = 8
10/x = 5
x = 2.
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Re: D01-28 [#permalink] New post   25 Oct 2017, 04:53
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks
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Re: D01-28 [#permalink] New post   25 Oct 2017, 05:10
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Kamran23Z wrote:
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks


\(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\).

(time)(combined rate) = (job done).
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Re: D01-28 [#permalink] New post   22 Sep 2018, 20:34
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you
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Re: D01-28 [#permalink] New post   23 Sep 2018, 03:50
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leonsandcastle332 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you


Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.


After you get \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\), only simple algebraic manipulations are left to be done:

\(\frac{1}{10}+\frac{1}{5}+\frac{1}{x}=\frac{4}{5}\)

\(\frac{1}{x}=\frac{4}{5}-(\frac{1}{10}+\frac{1}{5})\)

\(\frac{1}{x}=\frac{5}{10}\)

\(x = 2\).

Hope it's clear.
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Re: D01-28 [#permalink] New post   23 Sep 2018, 06:50
Bunuel wrote:
leonsandcastle332 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Please show how to solve for "X" once the last equation is setup. Thank you


Why is the question of poor quality? That's not right. Both the question and the solution are correct and detailed enough.


After you get \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\), only simple algebraic manipulations are left to be done:

\(\frac{1}{10}+\frac{1}{5}+\frac{1}{x}=\frac{4}{5}\)

\(\frac{1}{x}=\frac{4}{5}-(\frac{1}{10}+\frac{1}{5})\)

\(\frac{1}{x}=\frac{5}{10}\)

\(x = 2\).

Hope it's clear.


I apologize. I was stuck on something very dumb last night. Is there a way to change my feedback?
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Re: D01-28 [#permalink] New post   27 Dec 2018, 13:23
I think this is a high-quality question and I agree with explanation. I feel we take too long to answer this kind of question (in general), despite being simple math.
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Re: D01-28 [#permalink] New post   23 Jun 2020, 05:34
I think this is a high-quality question and I agree with explanation.
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Re: D01-28 [#permalink] New post   02 Oct 2020, 05:03
I think this is a high-quality question and I agree with explanation.
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Re: D01-28 [#permalink] New post   27 Oct 2020, 21:37
I think this is a high-quality question and I agree with explanation.
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Re: D01-28 [#permalink] New post   05 May 2023, 11:29
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re D01-28 [#permalink] New post   09 Aug 2023, 09:23
I think this is a high-quality question and I agree with explanation.
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Re: D01-28 [#permalink] New post   30 Sep 2023, 19:42
Bunuel wrote:
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?

A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)


Bunuel could we solve this question as a single algebraic equation, taking 't' as A's time, (t-2) for B, (t-4) for C and then solving it?

TIA for your explanation!
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Re: D01-28 [#permalink] New post   01 Oct 2023, 01:04
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ritwick2 wrote:
Bunuel wrote:
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?

A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)


Bunuel could we solve this question as a single algebraic equation, taking 't' as A's time, (t-2) for B, (t-4) for C and then solving it?

TIA for your explanation!


We know the value of t is 2 + 2 + 1/4. So, there's no need for an extra variable. The equation would simply be 2*1/10 + 2*(1/10 + 1/5) + 1/4*(1/10 + 1/5 + 1/x) = 1
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Re: D01-28 [#permalink] New post   23 Oct 2023, 03:34
Thank you for this! It really helps. Is there any material available that focuses on such work related problem?
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Re: D01-28 [#permalink] New post   23 Oct 2023, 03:39
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Su99 wrote:
Thank you for this! It really helps. Is there any material available that focuses on such work related problem?


17. Work/Rate Problems



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Re: D01-28 [#permalink]
23 Oct 2023, 03:39
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