Francois, I think you should consider posting the answer choices when you post your problem solving Qs for the reasons below.

1) Some people want to use the questions posted and the clock tool to test themselves as if they were on the GMAT. With no answer choices, one cannot simulate a GMAT question.

2) By hiding the answer choices, you force every solution provided to be an algebraic solution. On the GMAT however, the algebraic solution is not always the most efficient solution. Sometimes plug-in, reverse engineering, ballparking... are better option than the traditional solution. Since you do not post answer choices, we cannot always tell you the best way to approach a question.

That said, below is the solution
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Concept 1: Rate and time it takes to complete 1 job are inverses.
Concept 2: Combined rate is the sum of individual rates.
Concept 3: work = rate * time --> t=w/r

Since Jose and Jane take 20 days to complete 1 job, their combined rate is the inverse, so Jose_rate + Jane_rate = 1/20. Thus we can say that Jose's rate is 'r', and Jane's rate is (1/20 - r)

Jose does half the job. time = work/rate, so the time it took him is (1/2)/r = (1/2r)
Jane does the other half of the job. The time it took her (work/rate) is (1/2)/(1/20 - r) = 10/(1-20r)

We know that the total time is 45 days, so the sum of these times is 45: (1/2r) + 10/(1-20r) = 45. We can solve for r, Jose's rate. You will find that r = 1/30 or 1/60

Since we know that Jane is more efficient, Jose's rate will be the lower rate, or 1/60.

According to concept 1, if Jose's rate is 1/60, the time it would take him to do the job is 60 days. This is the answer

Hope that helps,
-Patrick

We can use the combined work formula combined with some critical reasoning.

Let Jose's time to complete the job working by himself be x. Let the same for Jane be y.

Then,

Txy = Tx*Ty/(Tx+Ty) [the combined time it takes 2 workers to complete a job is equal to the product of their individual times divided by the sum]

Then:

20 = Tx*Ty/(Tx+Ty)

We know that working by themselves, and each completing half of the job takes 45 days. Thus, the sum of the individual times for each to complete the job is 90 days, or Tx+Ty = 90

So:

20 = Tx*Ty/(90), and we also know that Tx = 90 - Ty, so:

20 = [(90-Ty)*Ty]/90, or:

Ty^2 - 90*Ty + 1800 = 0

2 numbers that multiply to 18 and add to 9 are 6 and 3. Thus, 2 numbers that multiply to 1800 and add to 90 are 60 and 30. But we know that Jose is less efficent, thus Jose's time to finish the job working by himself must be 60 days.

__________

francois, please always post the answer choices!

Nuts!

Patrick hit the "submit" button before me!

Oh well, at least you have 2 (very closely related) approaches now, francois.

Testluv wrote:Nuts!

Patrick hit the "submit" button before me!

Oh well, at least you have 2 (very closely related) approaches now, francois.

Deepak Dada,

Now I can see why u named ur username as " TestLuv". U still not lost the "competitive spirit"..Cheers

gmatmachoman wrote:

Testluv wrote:Nuts!

Patrick hit the "submit" button before me!

Oh well, at least you have 2 (very closely related) approaches now, francois.

Deepak Dada,

Now I can see why u named ur username as " TestLuv". U still not lost the "competitive spirit"..Cheers

Govi, sir.

You're right, I luv tests!

But I just meant that because Patrick's approach was so great, I likely wouldn't have posted had I actually seen it.

Don't you think its more than 2 min job ??

OA is below
y2 - 90 + 1800 = 0.
Factorizing and solving for y, we get y = 60 or y = 30.

If y = 60, then x = 90 - y = 90 - 60 = 30 and
If y = 30, then x = 90 - y = 90 - 30 = 60.

As the question clearly states that Jane is more efficient than Jose, the second answer is the only possible alternative.

Hence, Jose will take 60 days to complete the task if he worked alone and Jane will take only 30 days to complete the same task.

Testluv wrote: But I just meant that because Patrick's approach was so great, I likely wouldn't have posted had I actually seen it.

Dude, like everyone else here I wish I had your score!

The time it took her (work/rate) is (1/2)/(1/20 - r) = 10/(1-20r)

patrick how do you get 10/(1-20r) ?
(1/2)/(1/20 - r) is equal to 10 - r/ 2???

i think Gmat have one question and 5 options. in many cases even if options are sufficient to answer the question. so its no meaning discussing question without options. so kindly write options also

pradeepkaushal9518 wrote:i think Gmat have one question and 5 options. in many cases even if options are sufficient to answer the question. so its no meaning discussing question without options. so kindly write options also

I agree that the answer choices would allow us to have a more GMAT-specific discussion

francoisph wrote:The time it took her (work/rate) is (1/2)/(1/20 - r) = 10/(1-20r)

patrick how do you get 10/(1-20r) ?
(1/2)/(1/20 - r) is equal to 10 - r/ 2???

Simplify the denominator (1/20 - r) --> 1/20 - 20r/20 --> (1-20r)/20

The numerator is (1/2). To divide by a fraction, multiply by its reciprocal: (1/2) / (1-20r)/20 --> (1/2) [20/(1-20r)] --> 10/(1-20r)

-Patrick