Time and Work
Algebra
Level
3
5 men can do a work in 15 days. 5 men and 5 women can finish the same work in 10 days. In how many days 1 women can finish the work alone?
The answer is 150.
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1 solution
Since 5 men can do the job in 15 days, equivalent to 75 man days, then each man singly can perform 1/75 of the job each day. We also know that 5 men and 5 women can do the job in 10 days. This permits setting up the equation as follows: 5(1/75)(10) + 5(x)(10) = 1 where x= fraction of work done in 1 day by 1 woman, each 5 represents the number of men and women involved, and 10 is the number of days worked. 1 represents the fraction of work completed, i.e., 100%.
Solving the above equation results in x = 1/150. So it would take 1 woman 150 days to complete the job.