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Working together, Jose and Jane can complete an assigned

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Director
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Working together, Jose and Jane can complete an assigned [#permalink] New post 09 Apr 2007, 19:23
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completes half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if if he worked alone? Assume that Jane is more efficient than Jose.

Please show ALL work

Last edited by ggarr on 09 Apr 2007, 20:30, edited 1 time in total.
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Re: Work II [#permalink] New post 09 Apr 2007, 19:46
ggarr wrote:
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completes half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if if he worked alone? Assume that Jane is more efficient than Jose?

Please show ALL work


No answer choices?

Let Jose finish work in x days and Jane in y days. So to finish half task jose will take x/2 days and Jane will take y/2 days.

By given info we have x/2 + y/2 = 45 or (x + y) = 90 ---(1)---

Also when both work together we have 1/x + 1/y = 1/20
or (x+y)/xy = 1/20
0r xy = 20 * (x + y) = 1800

Since jane is efficient this means x > y

we know (x - y)^2 = (x + y)^2 - 4xy
or (x - y)^2 = 8100 - 7200 = 900
or x - y = 30
Since x + y = 45 on solving we get x = 75/2 = 37.5 and y is 7.5
Director
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 [#permalink] New post 09 Apr 2007, 20:31
The answer choices are:
25 days
30 days
60 days
65 days
36 days
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 [#permalink] New post 09 Apr 2007, 20:50
Assume:

Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day

Together, they does (x+y)/xy job in a day. This is equals to 1/20. So

(x+y)/xy = 1/20
20(x+y) = xy

Next, we're told 1 job takes 45 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.

x/2 + y/2 = 45
x+y = 90

So
xy = 1800

The answer choices are:
25 days
30 days
60 days
65 days
36 days

From the answer choices, 25,30 and 36 days are out since they result in Jane being less efficient. 65 days gives a fractional days (technically allowed, but I think we're thinking of whole numbers). So I'll go for 60 days for Jose and 30 days for Jane.
Director
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 [#permalink] New post 11 Apr 2007, 12:09
I'm sorry, but where did you get 1800 from?
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 [#permalink] New post 11 Apr 2007, 12:37
jose = x days
jane = y days

Jose rate = Rx = 1/x
Jane rate = Ry = 1/y

Rx+y = 1/20

Let Tx be the time for Jose to finish the work by himself. When half the work is done,
Rx = (1/2)/Tx
Ry = (1/2)/(45-Tx)

Rx+y = Rx + Ry
1/20 = 1/2*Tx + 1/2*(45-Tx)

Solve for Tx,
Tx = 30 or 15 days

If Tx = 15 days, then Ty = 30 days. Not possible since Jane is more efficient than Jose.

Tx = 30 days.

That is for half the work. For the entire amount, Tx = 60days.
  [#permalink] 11 Apr 2007, 12:37
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