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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?

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?

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

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. .
_________________

Please give me kudos, if you like the above post. Thanks.

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 [ 5.77 KiB | Viewed 8017 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]

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

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.

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?

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!!

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?

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.

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 _________________

“The best time to plant a tree was 20 years ago. The second best time is now.” – Chinese Proverb

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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