arjtryarjtry wrote:
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?
A. 6
B. 10
C. 8
D. 7.5
E. 3.5
Solution:We see that John’s rate is 1/20 and Jane’s rate is 1/12.
Letting t = the number of days it takes to get the work completed, we can create the equation:
(1/12) (t - 4) + (1/20) t = 1
Multiplying the equation by 60 we have:
5t - 20 + 3t = 60
8t = 80
t = 10
Alternate Solution:Since Jane quits 4 days before the job was completed, John worked alone for four days to complete the job. As it takes 20 days for him to complete the whole job, he can complete 1/5 of the job in 4 days. This means that together, they completed 1 - 1/5 = 4/5 of the job.
Since they can complete 1/12 + 1/20 = 8/60 = 2/15 of the job in one day; it will take them (4/5)/(2/15) = 6 days to complete 4/5 of the job. Together with the 4 days John worked alone, it took 6 + 4 = 10 days from the time the two started working together to complete the job.
Answer: B _________________
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