Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose works alone and completes half the work and then Jane takes over the task and completes the second half of the task, then task will be completed in 45 days. How long will Jose take to complete the task if he works alone, assuming that Jane is more efficient than Jose?
Answers
Answer:
Asha will take 60 days to complete the task if she worked alone
Step-by-step explanation:
Let say Asha can complete the work in A Days
& Sudha can complete the work in S days
Sudha is more efficient than Asha. => S < A
Asha and Sudha can complete together in 20 Days
=> 1/A + 1/S = 1/20
=> S + A = SA/20
=> 20S + 20A = SA
A/2 + S/2 = 45
=> A + S = 90
=> S = 90 - A
=> 20(90 - A) + 20A = (90- A)A
=> 1800 - 20A + 20A = 90A - A²
=> A² - 90A + 1800 = 0
=> A² - 30A - 60A + 1800 = 0
=> A(A - 30) - 60(A - 30) = 0
=> (A - 30)(A - 60) = 0
=> A = 30 or 60
S = 60 or 30
as Sudha is more efficient than Asha.
=> Asha will take 60 days to complete the task if she worked alone
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