A child can do a piece of work 15 hours slower than a woman. The child works for 18 hours on the job and then the woman takes over for 6 hours. In this manner, of the work is completed. To complete the job now, how much time would the woman take?
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Answer:
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Woman will take 15 hrs alone to complete work
Step-by-step explanation:
Let say Woman Complete work in W hrs
then Child Complete work in W + 15 hrs
Woman 1 hr work = 1/W
Child 1 Hr Work = 1/(W + 15)
Work done by child in 18 hrs = 18/(W+ 15)
Work done by woman in 6 hrs = 6/W
18/(W+ 15) + 6/W = 1
=> 18W + 6W + 90 = W² + 15W
=> W² - 9W - 90 = 0
=> W² - 15W + 6W - 90 = 0
=> W(W - 15) + 6(W - 15) = 0
=> (W - 15)(W + 6) = 0
=> W = 15
Woman will take 15 hrs alone to complete work
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