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M25 #16

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M25 #16 [#permalink] New post 04 Nov 2008, 20:16
Jack can complete the task in 8 hours. Tom can complete the 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

[Reveal] Spoiler: OA
D

Source:GMAT Club Tests - hardest GMAT questions

Together Jack and Tom will finish task in 4.8 hrs. When Tom joined in the task, half of the work was already done. So, Tom and Jack worked together for 4.8/2 = 2.4 hrs.

I don't understand why it is 4.8/2 hrs. Can someone please help to explain?

Thanks very much!!!
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Re: M25 #16 [#permalink] New post 04 Nov 2008, 22:18
Tom and Jack require 4.8 hours to finish the complete job. Hence, in order to finish half of the job, they will require half of the time = 4.8/2
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 05:18
Jon has worked for 4 hrs.He could have completed 1/2 of the work.Then Tom is joining and then they both can complete the work in 2.4 hrs.

So in total Jon could have worked for 4 + 2.4 = 6.4 hrs.

I will go with option D) 6.4
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 11:28
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Jack and Tom each worked x hours to finish 1/2 of the work.
x/8 + x/12 = 1/2
=> x=2.4hrs
Total hours by Jack = 4+2.4 = 6.4hrs (D)
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 12:02
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because of the spacing of the answer choices its really easy to guesstimate the answer without doing any real math. If jack worked for 4 hours half of it is done, and since tom takes more hours than jack to do the same work to do the remaining half jack has to work more than 6 hours. so choice a b c are out. And with E the ratio of jack to tom is not so lopsided that jack needs to do more than 75% of the work so the answer has to be D
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 17:31
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Hey ZMAT,
To understand the solution, I think you will require the following concepts cleared:
The formula for work problems is Work = Rate × Time, or W = R × T . The amount of work done is
usually 1 unit. Hence, the formula becomes 1 = R × T . Solving this for R gives R = 1/T.

Now keeping the above concept in mind, let us try to solve the problem.
-Jack can complete the task in 8 hours, so if he worked for 4 hours alone in the task then the task was half completed.
-If half the task is remaining, then Jack and Tom can complete half the task in half the time or in:
1/(1/6+1/4)=24/10=2.4hours.
-So the total time Jack takes to complete the problem is 4+2.4 = 6.4 hours.

I hope this helps.
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 19:01
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ANS : D

Rj=1/8
Rt=1/12
Rj+Rt=5/24

in 4 hour tom can complete =1/2

so,jointly they have to work to complete remaining =1/2

5/24*T=1/2
T=2.4

so total time Tom work = 4+2.4=6.4
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Re: M25 #16 [#permalink] New post 25 Jun 2010, 22:43
I always try to start with a basic translation of the words to math.
I drew a picture like the attached one, to make sure I don't end up giving the correct answer to the wrong question.
Attachment:
GMATQofDayJune25.JPG
GMATQofDayJune25.JPG [ 5.77 KiB | Viewed 6967 times ]

So the question is [Hours Jack Alone] + [Hours Jack with Tom] = ???

The questions gives you [Hours Jack Alone] = 4

Jack is half finished. He has worked 4 hours, and he would need 8 to finish. 4/8= .5

So we need to figure out [Half the task] / [Jack with Tom] = ??

I added the two hourly rates
*Jack completes 1/8 of the task
*Tom completes 1/12 the task

1/8 + 1/12 = 5/24 of the task each hour

.5 / [5/24] = .5 * 24 / 5 = 12/5 = 2 and 2/5 hours = [Hours Jack with Tom]

4 + 2.4 = 6.4
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Re: M25 #16 [#permalink] New post 26 Jun 2010, 08:54
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Hi guys
i got reminded of a shortcut formula (i came across long time ago) for this type of tasks:

A- Jack
B -Tom

Time taken if both together completes the task = AB/A+B
so if tom and jack works together, time = 8x12/8+12 =96/20=4.8

In this problem we need to go little further..
Jack already completed half = 4 hrs
Rest half work together(Jack+Tom) = 4.8/2 = 2.4
so total time spent by Jack = 4 +2.4 = 6.4

voila :)
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Re: M25 #16 [#permalink] New post 26 Jun 2010, 13:16
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Here is how I solved it:

Let x be the time they both work together.. so set up an equation

Jack has worked for 4 hours plus x and tom has worked for only x hours. Sum of both the time taken is always equal to one.

4+x/8 +x/12=1

When you solve you will get x= 2.4. Add 2.4 to 4 which equals 6.4
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Re: M25 #16 [#permalink] New post 22 Jul 2010, 13:33
D

Breezer... however I sat on this question for a good 5 minutes w/o concentration.

Time taken by Jack alone to complete the Job (J1) = 8 hours
Time taken by Tom alone to complete the Job (J1) = 12 hours

Now Jack starts working on J1.... works for 4 hours ie. 1/2 of the time that Jack normally takes to complete J1.

After the first 4 hours job J1 is half done.


Time taken by Jack alone to complete the second half of Job (J1) = 8/2 = 4 hours
Time taken by Tom alone to complete the second half of Job (J1) = 12/2 = 6 hours

Work done by Jack in one hour on the second half of the job = 1/4
Work done by Tom in one hour on the second half of the job = 1/6

Work done together in one hour on the second half of the job = 1/4 + 1/6 = (4+6)/24 = 10/24

Time taken to complete the second half of the job by Jack and Tom together = 24/10 = 2.4 hours

Total time taken = Time taken by Jack to finish the first half of the job + time taken by Jack and Tom together on the second half.

= 4 + 2.4
=6.4 hours
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Re: M25 #16 [#permalink] New post 30 Jun 2011, 01:18
It can also be a ans --

let the time for which tom worked be x
so time for jack = x+4

now rate= work* time

forming equation :-
(jack's rate ) + (tom's rate)=1

1/8*(x+4) + 1/12*x=1

x=2.4

total time jack worked = 4+2.4= 6.4

thanks if u like the way in which it is solved!!
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Re: M25 #16 [#permalink] New post 30 Jun 2011, 02:19
In 4 hours, Jack does 0.5 of the work.

Working together, both take \frac{(1}{8) + (1/12) = 5/24 or 4.8 hours}. The remaining 0.5 of the task will be done in 2.4 hours.

Total will be 6.4 and answer should be D.
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Re: M25 #16 [#permalink] New post 01 Jul 2011, 11:50
sessmi wrote:
Jack can complete the task in 8 hours. Tom can complete the 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

[Reveal] Spoiler: OA
D

Source:GMAT Club Tests - hardest GMAT questions

Together Jack and Tom will finish task in 4.8 hrs. When Tom joined in the task, half of the work was already done. So, Tom and Jack worked together for 4.8/2 = 2.4 hrs.

I don't understand why it is 4.8/2 hrs. Can someone please help to explain?

Thanks very much!!!




Ok I will give my 2 cents also here,
one of the best approach for work problems is the one used by varun,
I will explain it using my own words,

we know that:
1) jack will complete 1/8 of work in 1 hour
2) tom will complete 1/12 of work in 1 hour

(trying to have everything related to an hour as common measure)

3) together they will have a work rate of 5/24 in an hour (obtained by adding the two rates 1/8 + 1/12)

4) we know that after 4 hours jack will complete 1/2 of work (it is given on the question stem)

5) 1/2 (resto fo work to be done) divided by 5/24 (ratio of tom and jack together) will give us 2.4 hour

6) add 2.4 hrs to 4 hrs (time spent from jack to work alone) we got 6.4 answer d

time needed around 40 -60 secs top...

for those who are new on this forum I highly recommend to check this blw post from sriharimurthy,


work-word-problems-made-easy-87357.htm (it does not let me post it)

it helped and helps me a lot


hope my post helped you,

Yes we Can get and High score,
Be perseverant and win!!



sriharimurthy work-word-problems-made-easy-87357.html#p656651
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Re: M25 #16 [#permalink] New post 27 Mar 2012, 02:49
Expert's post
sessmi wrote:
Jack can complete the task in 8 hours. Tom can complete the 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

[Reveal] Spoiler: OA
D

Source:GMAT Club Tests - hardest GMAT questions

Together Jack and Tom will finish task in 4.8 hrs. When Tom joined in the task, half of the work was already done. So, Tom and Jack worked together for 4.8/2 = 2.4 hrs.

I don't understand why it is 4.8/2 hrs. Can someone please help to explain?

Thanks very much!!!


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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Re: M25 #16 [#permalink] New post 03 Jul 2012, 03:09
Jack's efficiency= 12.5%
Tom's efficiency= 8.33%

Jack works for 4 hours= 12.5*4= 50% work complete

Jack and Tom's cumulative efficiency= 12.5+8.33= 20.83%

Time taken to complete the work pending, together= 50/ 20.83= 2.4 hours

Jack's total time = 4 hours + 2.4 hours = 6.4 hours.
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Re: M25 #16 [#permalink] New post 03 Jul 2012, 04:13
Answer is D.

After Jack's 4 hour input, half of the work remains. Therefore Jack's total input = 4+time both fellas worked (let's call that joint time "t")

Therefore [(1/12)+(1/8)]*t=1/2
t===>2.4hrs
Jack's total input=4.0+2.4=6.4

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Re: M25 #16 [#permalink] New post 03 Jul 2012, 06:42
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The answer is D-6.4 hrs

Jack's rate of working = 1/8 work/hr
Tom's Rate of work = 1/12 work/hr

Jack works for 4 hours first --> so r.t=w -> (1/8).4 = w => 1/2 ( half the work is done by Jack in those 4 hrs)

Now when both start working together rate of work is = (1/8)+(1/12)

Time taken to finish the remaining half of the work is = (r.t=w) -> {(1/8)+(1/12)}.t = 1/2
-> t= 2.4 hrs

Therefore Jack work 4 hrs alone and then 2.4 hours with Tom -> So, Total hours worked by Jack = 4+2.4= 6.4 Hrs
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Re: M25 #16 [#permalink] New post 04 Jul 2012, 03:06
Jack - 8 hrs - in 1 hr - 1/8 Tom - 12 hrs - in 1 hr- 1/12
Jack works for 4 hours so he does 1/8/4 = 1/2 and 1/2 is left
In one hour work done by Jack and tom : ab/a+b = 8*12/8+12 = 24/5 = 4.8
In one hour - 24/5 so in how many hour 1/2 = 24/5*1/2 = 24/10 = 2.4 hrs
so earlier 4 + 2.4 hrs = 6.4 hrs Answer D
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Re: M25 #16 [#permalink] New post 31 Aug 2012, 19:36
This question took me 2mins 2 secs which I feel is on the higher side. I need to work further on reducing the time taken because I knew the approach but just kind of missed a trick at the last point of the solution.

I followed a similar approach as per the work formula. My solution goes as follows --:

Jack : 8 hours to complete the job. Hence in 4 hours he will complete 1/2 of the job.

At this point Tom (who takes 12 hours for the job) joins in.

Together, Jack and Tom complete (1/8+1/12) of the job is 1 hour i.e. 5/24 of the job in 1 hour.

Here, I missed a simple trick i.e. 5/24 in 1 hour hence 24/5 for the entire job i.e. (24/5)/2 for half the job. This could have reduced my time about 10-15 secs.

I spent relatively longer time on this step. Since we need time for 1/2 of the job i.e. 12/24 it can be split as 5/24+5/24+2/24 i.e. 1 hour + 1 Hour + <~half hour.

Hence total time needed by Jack = 4 hours + ~2.5 Hours = greater than 6 hours but less than 6.5 hours. D is the only option hence I chose D.
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Re: M25 #16   [#permalink] 31 Aug 2012, 19:36
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