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Jack and tom

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by j_shreyans » Fri Sep 05, 2014 9:27 pm
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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by GMATinsight » Fri Sep 05, 2014 10:01 pm
j_shreyans wrote: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

OAD
Let's assume that total amount of work = 48

Jack's 1 hour work = 48/8 = 6 Units
Tom's 1 hour work = 48/12 = 4 Units

Jack's 4 hour work = 4 x6 Units = 24 Units

Remaining work = 48-24 = 24 Units

Now Jack and Tom's 1 hour work (together) = 6+4 = 10 Units
Remaining time needed = 24/10 = 2.4 days

Total days that Tom worked = 4+2.4 = 6.4 Days

Answer: Option D
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by GMATGuruNY » Fri Sep 05, 2014 10:53 pm
j_shreyans wrote: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
Let the task = 24 units.

Since Jack can complete the task in 8 hours, Jack's rate = w/t = 24/8 = 3 units per hour.
Since Tom can complete the task in 12 hours, Tom's rate = w/t = 24/12 = 2 units per hour.
Combined rate for Jack and Tom working together = 3+2 = 5 units per hour.

Work completed by Jack working alone for 4 hours = r*t = 3*4 = 12 units.
Remaining work = 24-12 = 12 units.
At a combined rate of 5 units per hour, the time for Jack and Tom to complete the remaining 12 units = w/r = 12/5 hours.

Total time for Jack = (Jack's time alone) + (Jack's time working with Tom) = 4 + 12/5 = 4 + 2.4 = 6.4 hours.

The correct answer is D.
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by Brent@GMATPrepNow » Sat Sep 06, 2014 6:29 am
j_shreyans wrote: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
I would solve this question using the same technique shown by Mitch and Bhoopendra. However, can also solve it by applying the following 2 rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let's use these rules to solve the question. . . .

Jack can complete the task in 8 hours. Tom can complete the same task in 12 hours.
Applying Rule #1, we know that, in ONE HOUR, Jack can complete 1/8 of the task, and TOM can complete 1/12 of the task.
If we COMBINE their efforts, we see that in ONE HOUR they can complete (1/8 + 1/12) of the job.
1/8 + 1/12 = 5/24, So, in IN ONE HOUR they can complete 5/24 of the job

If we apply Rule #2, we see that it will take Tom and Jack 24/5 hours to COMPLETE the job.
In other words, it will take Tom and Jack 4.8 hours to complete the ENTIRE job.

Of course, Tom and Jack aren't working together for the ENTIRE job.
We're told that Jack works on the task alone for 4 hours
Since Jack can complete the task in 8 hours, we can conclude that he completes HALF of the task in this time.

So, Tom and Jack work together for only HALF the job.
Well, if they can complete the ENTIRE job in 4.8 hours, then they can complete HALF the job in 2.4 hours.

So, JACK's total time = (his initial 4 hours alone) + (2.4 hours with Tom)
= 6.4
= D

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by Matt@VeritasPrep » Sat Sep 06, 2014 9:04 am
I would actually avoid using work units here, as it adds an unnecessary element to the problem.

Instead, just consider it this way.

Jack's Rate = 1/8 of the job per hour
Tom's Rate = 1/12 of the job per hour

Jack works for 4 hours alone. Since Work = Rate * Time, we can say Jack's Work = 1/8 * 4, since Jack's Rate = 1/8 and his initial Time = 4 hours. 1/8 * 4 = 1/2, so Jack does 1/2 of the job alone.

This means we have 1/2 of the job left. Jack and Tom are working TOGETHER, so we can add their rates. This gives us

Work = 1/2
Rate = 1/8 + 1/12 = 5/24

Work = Rate * Time, so 1/2 = 5/24 * T. This gives us T = 12/5, so the two guys work TOGETHER for 12/5 of an hour.

Since Jack worked for 4 hours alone and 12/5 hours with Tom, he worked for a total of 4 + 12/5 hours, or 4 + 2.4, or 6.4 hours.
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by GMATinsight » Sat Sep 06, 2014 9:18 am
j_shreyans wrote: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

OAD
Another interesting way to look at the problem step-by-step

Line 1: Jack can complete the task in 8 hours
Line 2: Jack works on the task alone for 4 hours --- Which means that he finishes half of work

Remaining work = 1/2

Now,
Line 3: Tom can complete the same task in 12 hours
Line 4: Jack and tom work together for X hour, total work done by them together = X(1/8 + 1/12) = X(5/24)
But X(5/24) = 1/2 ==> X = 12/5 ==> X=2.4

Total Time = 4+2.4 = 6.4 Days

Answer: Option D
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