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M28-19

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M28-19  [#permalink]

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New post 16 Sep 2014, 01:29
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A
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C
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Difficulty:

  45% (medium)

Question Stats:

70% (02:07) correct 30% (02:40) wrong based on 182 sessions

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Three workers, A, B, and C, can complete a certain task in 10, 5 and \(x\) hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C 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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New post 16 Sep 2014, 01:29
Official Solution:

Three workers, A, B, and C, can complete a certain task in 10, 5 and \(x\) hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C 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 \(2*\frac{1}{10}=\frac{1}{5}\) of the taks will be done (as only A works);

After 4 hours \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task will be done and \(\frac{1}{5}\) will be left to be done;

We are told that \(\frac{1}{5}\)th of the task is done in 15 minutes (1/4th of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From which we can find that \(x=2\) hours.


Answer: C
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Re: M28-19  [#permalink]

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New post 21 Sep 2014, 00:29
2
There seems to be a typo with the question stem.( hours/mins)
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New post 21 Sep 2014, 01:17
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Re: M28-19  [#permalink]

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New post 22 Sep 2014, 12:40
1/10 * 17/4 + 1/5 * 9/4 + 1/x * 1/4 = 1

[17/4 is 4 hr & 15 min ; 9/4 is 2 hrs & 15 min]

Solve -> x = 2
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Re: M28-19  [#permalink]

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New post 16 Nov 2018, 08:06
Bunuel wrote:
Official Solution:

Three workers, A, B, and C, can complete a certain task in 10, 5 and \(x\) hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C 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 \(2*\frac{1}{10}=\frac{1}{5}\) of the taks will be done (as only A works);

After 4 hours \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task will be done and \(\frac{1}{5}\) will be left to be done;

We are told that \(\frac{1}{5}\)th of the task is done in 15 minutes (1/4th of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From which we can find that \(x=2\) hours.


Answer: C

I think I know the concept testing here but I want a more generalized approach. Can you explain it in details or any other way?

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New post 12 Jan 2019, 17:20
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. I do not understand how 1/4*(1/10+1/5+1/x) gives you 2 hours unless I just plug in answers at random.
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New post 13 Jan 2019, 01:00
granadylan wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. I do not understand how 1/4*(1/10+1/5+1/x) gives you 2 hours unless I just plug in answers at random.


This is really a very simple algebra.

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

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

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

\(\frac{1}{x}=\frac{1}{2}\).

\(x=2\).
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New post 24 Jan 2019, 05:14
We can solve it with LCM method as well

Let's assume LCM for 10, 5 and x to be 10x. Our whole job will consist of 10x units
So:
A in 1 hour will make \(\frac{10x}{10}\)=x units
B in 1 hour will make \(\frac{10x}{5}\)=2x units
C in 1 hour will make \(\frac{10x}{x}\)=10 units

First 2 hours: A is working alone, so 2x units are done
Following two hours: A and B are working, so 2*3x=6x units are done

During first 4 hours 2x+6x=8x units are done and 10x-8x=2x units are left to be done

A, B and C working together did the remaining 2x units in \(\frac{1}{4}\) hour
\(\frac{10+3x}{4}\)=2x
x=2

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M28-19   [#permalink] 24 Jan 2019, 05:14
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