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Working individually, Deborah can wash all the dishes from her friend’

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Working individually, Deborah can wash all the dishes from her friend’ [#permalink]

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New post 26 Nov 2014, 06:40
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Tough and Tricky questions: Work/Rate Problems.



Working individually, Deborah can wash all the dishes from her friend’s wedding banquet in 5 hours and Tom can wash all the dishes in 6 hours. If Deborah and Tom work together but independently at the task for 2 hours, at which point Tom leaves, how many remaining hours will it take Deborah to complete the task alone?

A. 4/15
B. 3/11
C. 4/3
D. 15/11
E. 11/2

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New post 26 Nov 2014, 06:58
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Bunuel wrote:

Tough and Tricky questions: Work/Rate Problems.



Working individually, Deborah can wash all the dishes from her friend’s wedding banquet in 5 hours and Tom can wash all the dishes in 6 hours. If Deborah and Tom work together but independently at the task for 2 hours, at which point Tom leaves, how many remaining hours will it take Deborah to complete the task alone?

A. 4/15
B. 3/11
C. 4/3
D. 15/11
E. 11/2

Kudos for a correct solution.

Source: Chili Hot GMAT


Deborah can complete the job in 5 hrs so one hour work is 1/5
Tom can complete the same job in 6 hrs so one hour work is 1/6
amount of work complete in in one hour by both working together = 1/5+1/6 = 11/30
they both work together for 2 hours , thus work done in 2 hrs = 22/30
work left = 1-(22/30) = 8/30
after 2 hrs tom left and the remaining work will be complete by Deborah
Deborah complete 1 work in 5 hrs, then 8/30 work will be completed in 5*8/30 hrs i.e 4/3
[C]
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Re: Working individually, Deborah can wash all the dishes from her friend’ [#permalink]

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New post 26 Nov 2014, 07:00
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First determine how many dishes Deborah and Tom can wash in two hours. From the question stem, we can see that Deborah can wash 1/5 of the dishes in one hour, and Tom can wash 1/6 of the dishes in one hour. Therefore, in two hours they can wash:

1/5 * 2 + 1/6 * 2 = 2/5 + 1/3 = 11/15 of the dishes

At this point Tom leaves, and there are 1 - 11/15 dishes = 4/15 of the dishes remaining to be washed

Again, from the question stem we can see that Deborah can wash 1/5 or 3/15 of the dishes in one hour, so it would take her slightly more than one hour to wash the remaining 4/15 dishes. At this point, you can eliminate A & B as answer choices since they are less than one. You can also eliminate E as an answer choice since it represents a number greater than 5 and we know from the question stem that Deborah can wash all the dishes in exactly 5 hours (so it wouldn't take her more than 5 hours to wash a fraction of the total number of dishes..).

You can set up an inequality to determine how long it would take Deborah to wash 4/15 of the dishes as follows:

If it takes her 1 hour to wash 3/15 of the dishes, how long would it take her to wash 4/15?

1/(3/15) = x/(4/15)

If you solve for x, you get 4/3 which is answer choice C.

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New post 26 Nov 2014, 10:54
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Together, they can finish the job in 1/5 + 1/6 = 1/T time. Solving for T yields 30/11 hours. If they've already worked for 2 hours, which is 22/11 hours, they have 22/30 done and about 4/15 of the job left. Going at a rate of 5 hours/job, Deborah can finish in 5hours/job*4job/15 = 4/3 hours.

Choice C

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Re: Working individually, Deborah can wash all the dishes from her friend’ [#permalink]

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New post 26 Nov 2014, 19:56
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In first 2 hrs Tome will finish 2/6 = 1/3 of work and Deborah will finish 2/5 work so total 1/3 + 2/5 = 11/15 work is finished and
1-11/15 = 4/15 work remaining. Now Deborah will take (4/15)*5 = 4/3 hrs to finish it.

So answer is C.

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New post 26 Nov 2014, 20:26
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Answer = C = 4/3

Rate of Deborah \(= \frac{1}{5}\)

Rate of Tom \(= \frac{1}{6}\)

Combined rate (Tom & Deborah) \(= \frac{1}{6} + \frac{1}{5} = \frac{11}{30}\)

Combined work done \(= \frac{11}{30} * 2 = \frac{11}{15}\)

Pending work\(= 1 - \frac{11}{15} = \frac{4}{15}\)

Time required by Deborah only for pending work \(= \frac{4}{15} * 5 = \frac{4}{3}\)
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Re: Working individually, Deborah can wash all the dishes from her friend’ [#permalink]

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New post 17 Oct 2017, 06:58
For Problems such as these, I prefer to use the RTW chart. To make calculations easier let the work done be 30 (LCM of 5 and 6).

The Table will look something like this

Attachment:
Screen Shot 2017-10-17 at 8.24.06 PM.png
Screen Shot 2017-10-17 at 8.24.06 PM.png [ 26.56 KiB | Viewed 395 times ]


From the RTW chart, it is clear that the time needed by Deborah to finish the Balance work is 4/3. Required answer is C.
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New post 10 Nov 2017, 22:29
We can avoid fractions
Total work= LCM of time taken by Deborah and tom=6*5=30=Total work

Formula=workdone(w)=Rate*Time
w=30
Time taken by Deborah=5hrs
Time taken by Tom=6hrs
Rate of Deborah=30/5=6 ie she does 6 units of work every Hr
Rate of Tom=30/6=5 ie he does 5 units of work every Hr
In 1 hr both of them can do 5+6=11 units of work and in 2 hrs they both can do 22 units of work.
The work left=30-22=8
Deborah can do this work in 8/6=4/3 hrs.

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Working individually, Deborah can wash all the dishes from her friend’   [#permalink] 10 Nov 2017, 22:29
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