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Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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Difficulty:   45% (medium)

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

### HideShow timer Statistics 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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Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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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.

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Intern  Joined: 06 Jun 2011
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2
There seems to be a typo with the question stem.( hours/mins)
Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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kishgau wrote:
There seems to be a typo with the question stem.( hours/mins)

Thank you. Edited.
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Intern  Joined: 04 Jul 2014
Posts: 46
Schools: Smeal" 20

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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
Intern  S
Joined: 05 Oct 2017
Posts: 46
Concentration: Accounting, Social Entrepreneurship

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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.

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?

Posted from my mobile device
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Intern  B
Joined: 11 Jan 2019
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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56300

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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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Senior Manager  G
Joined: 13 Feb 2018
Posts: 421
GMAT 1: 640 Q48 V28 ### Show Tags

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

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

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