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D01-28

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D01-28 [#permalink]

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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. \(4\)
[Reveal] Spoiler: OA

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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, 20:04
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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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New post 22 Mar 2017, 07:35
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, 07:48
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, 05:01
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, 03:53
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, 04:10
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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New post 25 Oct 2017, 21:50
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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Re: D01-28 [#permalink]

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New post 03 Nov 2017, 05:44
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] 03 Nov 2017, 05:44
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