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# M28-19

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Math Expert
Joined: 02 Sep 2009
Posts: 52344

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16 Sep 2014, 00:29
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:09) correct 31% (02:39) wrong based on 172 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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Joined: 02 Sep 2009
Posts: 52344

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16 Sep 2014, 00:29
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.

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Intern
Joined: 06 Jun 2011
Posts: 22

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20 Sep 2014, 23:29
2
There seems to be a typo with the question stem.( hours/mins)
Math Expert
Joined: 02 Sep 2009
Posts: 52344

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21 Sep 2014, 00:17
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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22 Sep 2014, 11:40
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
Intern
Joined: 05 Oct 2017
Posts: 40
Concentration: Accounting, Social Entrepreneurship

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16 Nov 2018, 07:06
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.

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
Joined: 11 Jan 2019
Posts: 2

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12 Jan 2019, 16:20
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.
Math Expert
Joined: 02 Sep 2009
Posts: 52344

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13 Jan 2019, 00:00
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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Re: M28-19 &nbs [#permalink] 13 Jan 2019, 00:00
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# M28-19

Moderators: chetan2u, Bunuel

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