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D01-28

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D01-28  [#permalink]

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New post 16 Sep 2014, 00:12
2
15
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (02:44) correct 36% (03:27) wrong based on 115 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, 00:12
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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 1/5th 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: D01-28  [#permalink]

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New post 31 Oct 2015, 21:04
2
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]

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New post 22 Mar 2017, 08:35
not clear why 1/4 has been multiplied at end
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Re: D01-28  [#permalink]

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New post 22 Mar 2017, 08:48
johncath wrote:
not clear why 1/4 has been multiplied at end


1 hour is 1.
15 minutes is 1/4
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New post 04 Jul 2017, 06:01
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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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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New post 25 Oct 2017, 05:10
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New post 25 Oct 2017, 22:50
Consider the total work as 10, and A can do 1 work in 1hr, B can do 2 work in 1 hr. A starts work for 2 hrs. So 2 work completed(1×2=2), then B joins for 2 hrs, so B does 4 work (2×2=4), now total work = A's 4+B's 4 work = 8. Balance work is 2. C joins and complete the work in 15 mins. That is A do .25 work and B do .5 work in15 mins., total .75 work(.25+.5=.75).Balace 1.25 work is done by C in 15 mins. So C can do 5 work in 1 hr. It means C takes 2hrs to complete the total work.
Ans : opt.c, 2hrs

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New post 03 Nov 2017, 06:44
10 A = 5 B =Cx= k = since work remain same that each does

10A = since work remains the same

10 A = A*2 + (A+B)2 + (A+B+C) *1/4

=> K = K/10 *2 + (K/10+K/5)2 + (K/10 + K/5 +k/x) *1/4

solving for above equation

=> 1/2 = 1/x

x =2 hours for C
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Re: D01-28  [#permalink]

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New post 30 Aug 2018, 22:15
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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New post 10 Sep 2018, 20:08
Hi Bunuel: Question M28-19 and D01-28 are the same. Just in case if it was not known earlier.
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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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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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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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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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New post 25 May 2019, 00:52
Can someone please explain this step?

After 4 hours 1/5+2∗(1/10+1/5)=4/5

How did we add up A's and B's works?
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New post 29 May 2019, 19:41
Hi Bunuel
Please identify the mistake in my approach.

A = 1/10 * 2 * 2 * 1/4 = 1/10
B = 1/5 * 2 * 1/4 = 1/10
C = 1/x * 1/4 = 1/x

1/10 + 1/10 + 1/x = 1

Of course, am not getting the answer, but what is my equation missing?

Thanks in advance. :please
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Re: D01-28   [#permalink] 29 May 2019, 19:41
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