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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?

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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

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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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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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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.

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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.

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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.