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# M25-16

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Math Expert
Joined: 02 Sep 2009
Posts: 45423
M25-16 [#permalink]

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16 Sep 2014, 01:23
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Difficulty:

5% (low)

Question Stats:

84% (01:20) correct 16% (01:47) wrong based on 230 sessions

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Jack can complete the task in 8 hours. Tom can complete the same task in 12 hours. If Jack works on the task alone for 4 hours and then Tom starts to help him, how many hours in total will Jack have worked by the time the task is finished?

A. 5.0
B. 5.2
C. 5.6
D. 6.4
E. 7.2

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Math Expert
Joined: 02 Sep 2009
Posts: 45423
Re M25-16 [#permalink]

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16 Sep 2014, 01:23
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Official Solution:

Jack can complete the task in 8 hours. Tom can complete the same task in 12 hours. If Jack works on the task alone for 4 hours and then Tom starts to help him, how many hours in total will Jack have worked by the time the task is finished?

A. 5.0
B. 5.2
C. 5.6
D. 6.4
E. 7.2

Since Jack can complete the task in 8 hours then in 4 hours that he works alone he does half of the task, so another half is has to be done. Combined rate of Jack and Tom working together is $$\frac{1}{8}+\frac{1}{12}=\frac{5}{24}$$ task/hour, so working together they can complete the task in $$\frac{1}{(\frac{5}{24})}=\frac{24}{5}$$ hours, which means that for half of the task they need another $$\frac{(\frac{24}{5})}{2}=\frac{24}{10}=2.4$$ hours.

Hence, the total time that Jack worked is $$4+2.4=6.4$$ hours.

Answer: D
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Joined: 11 Jun 2013
Posts: 1
Schools: IMD '16
Re: M25-16 [#permalink]

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15 Oct 2014, 07:21
Easier way to look at such problems is to think in terms of capabilities.

jack takes 8 hrs and Tom takes 12 hrs. So Tom has 2/3 the capacity of jack to complete the same work. In First 4 hrs tom completes half the work, remaining half work is done by Tom + Some one who is 2/3 as good as Tom , or in other words Tom +2/3 Tom = 5/3 Toms are working. So it should take (4)/(5/3) hrs to complete the remaining half.

This yields , 12/5 or 2.4 hrs .

So in total it will be 4+2.4 =6.4 hrs.
Intern
Joined: 29 Mar 2013
Posts: 28
Schools: ISB '16
Re: M25-16 [#permalink]

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01 Dec 2014, 20:42
for me it is:

W=Rate *Time
for 1st R=x/8
2nd R=x/4

First 4 only 1 worked.. i.e. W= x/8 *2 = x/2
Next 4 hours W remaining x/2 = x/8 + x/12 => 5x/12
Time = 1/(5/12) = 2.4
Total time 4+2.4 =6.4
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Joined: 26 Nov 2012
Posts: 599
M25-16 [#permalink]

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12 Sep 2017, 11:38
Jack can complete the task in 8 hours. Tom can complete the same task in 12 hours. If Jack works on the task alone for 4 hours and then Tom starts to help him, how many hours in total will Jack have worked by the time the task is finished?

A. 5.0
B. 5.2
C. 5.6
D. 6.4
E. 7.2

====================================================================================================

Jack's rate in one hour = 1/8

Tom's rate in one hour = 1/12

It is mentioned that Jack worked for 4 hours and Tom joined then work got completed. Now Tom worked for x hours and the same number of hours even Jack worked to finish the work (as Tom joined both worked for x hours )

Then we get the below as both worked to finish the same job.

$$\frac{x+4}{8}$$+ $$\frac{x}{12}$$ = 1

=> 5x +12 = 24
=> x = 2.4

Now total number of hours Jack worked is 4 + 2.4 = 6.4 hours..
M25-16   [#permalink] 12 Sep 2017, 11:38
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# M25-16

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