Work Problem

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hariharakarthi
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Topic: Work Problem
PostThu Nov 19, 2009 7:47 pm
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There are 80 flowers to be planted in the garden. Judy and Harry can complete the job together in four hours if they do not take a break. How long would it take Harry to complete the job alone?

(1) Judy plants 3 flowers in the time it takes Harry to plant 2.
(2) Judy working alone would take 6 hours to complete the job.

Please explain the ans in detail.
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PostThu Nov 19, 2009 9:19 pm
A??? I am not sure though. We know that they are not taking a break while planting the flowers. The work is done in the ratio of 3:2. So I guess we can find out from statement 1 that how much work are both of them doing.
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PostThu Nov 19, 2009 9:51 pm
The answer is D but the question is badly designed and would never appear on the GMAT: the statements contradict each other. Also, a true GMAT question would make clear that they would be working together but independently (if they set up some kind of assembly chain, then the combined rate of work could be super-additive).

In two-worker combined work problems, the time it takes two workers to do the job is equal to the product of the individual workers' times divided by the sum of the individual workers' times:

Time to do the job with A and B working together = Time for A alone *Time for B alone /(Time for A alone+ Time for B alone)

Let's take a look at the problem:

"There are 80 flowers to be planted in the garden. Judy and Harry can complete the job together in four hours if they do not take a break. How long would it take Harry to complete the job alone?"

The question tells us their combined time is 4 hours. (Incidentally, the fact that there are 80 flowers is irrelevant).

(1) Judy plants 3 flowers in the time it takes Harry to plant 2.

Because Judy works three-halves as fast as Harry, it would take Harry 3/2 as long to complete the same unit of work as Judy. Letting Judy's time be x, Harry's time is 3x/2, and plugging into the formula:

4 = (x*3x/2)/(x +3x/2)

Because we have only one unknown in our equation, the equation is solveable and the statement is sufficient. (Don't actually solve it because this is data sufficiency).


(2) Judy working alone would take 6 hours to complete the job.

This is sufficient because we can plug into the formula and solve for Harry's time.

The question is problematic because, in statement one, Judy's time to complete the job is 6 and two thirds of an hour. This clearly contradicts statement two. On the GMAT, the only assumption you are allowed to make in Data Sufficiency is: the statements will NEVER contradict. I would not practice on questions from this source.
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