John can complete a given task in 20 days. Jane will take

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John can complete a given task in 20 days. Jane will take [#permalink]

20 Jul 2008, 05:23

John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?

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Re: time and work [#permalink]

20 Jul 2008, 05:36

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10 days. Here is the explanation
for 4 days Jane didn't work, hence john would complete (4/20=1/5 of the work). Therefore Jane and John together will complete 4/5 of the work.
Now John and Jane together would complete the work in (1/20+1/12=15/2 days).
Therefore they would take 6 days to complete 4/5 of the work, after which John worked for another 4 days. Hence in total they took 6+4=10 days to complete.

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Re: time and work [#permalink]

20 Jul 2008, 05:53

R * T = 1

John's rate = 1/20
Jane's rate = 1/12

(1/20)T + (1/12)(T-4) = 1
T/20 + (T-4)/12 = 1
(12T + 20T - 80)/240 = 1
32T = 320
T=10

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Re: time and work [#permalink]

20 Jul 2008, 06:03

john's rate = 1/20
jane's rate = 1/12
combined rate = 1/20+1/12 = 2/15

let the work finished in x days
both woked for (x-4) days amd John alone worked for 4 days

(x-4)*2/15 + 4*1/20 = 1
2x - 8 + 3 = 15
x= 10 answer .............

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Re: time and work [#permalink]

20 Jul 2008, 07:04

I have a different point of view, solution can be too long, however, it is easy to think and solve with this method.

We know that John completes the task in 20 days, Jane completes the task in 12 days.
We can assume that total of this work is 60 units (which is the least common multiply)

From here; John finishes 3 units of the task in a day (60/20=3)
Jane finishes 5 units of the task in a day (60/12=5)

First 4 days, john complete 4*3=12 units of the task. Remaining part is 48 units (60-12=48)
Both of them complete 3+5=8 units of the task in a day. Accrodingly, they can complete 48 units of tasks in 6 days.

Then, the answer is 4+6=10...

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Re: time and work [#permalink]

20 Jul 2008, 20:51

explaination plz...................
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Every Problem Has a Sloution So keep working
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Re: time and work [#permalink] 20 Jul 2008, 20:51

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John can complete a given task in 20 days. Jane will take

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John can complete a given task in 20 days. Jane will take

John can complete a given task in 20 days. Jane will take

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