Question:
Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?
Correct Answer
14 910/2773 days or 14.328 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Carol = 42 days
And, the number of days required to finish the same work by Amanda = 43 days
And, the number of days required to finish the same work by Dorothy = 44 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 42 days the work is done by Carol = 1
∴ The work done by Carol in 1 day = 1/42
Similarly,
∵ In 43 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/43
Similarly,
∵ In 44 days the work is done by Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/44 part
Now, the work done by Carol, Amanda, and Dorothy together in 1 day
= Carol's 1 day work + Amanda's 1 day work + Dorothy's 1 day work
= 1/42 + 1/43 + 1/44
= 946 + 924 + 903/39732
= 2773/39732 part of work
This means in 1 day, 2773/39732 part of work is done by Carol, Amanda and Dorothy working together.
Now, the number of days required to finish 2773/39732 part of work by Carol, Amanda, and Dorothy working together = 1
∴ the number of days required to finish the whole work (1 work) by Carol + Amanda + Dorothy together
= 1/2773/39732
= 1 × 39732/2773 = 39732/2773 days
= 14 910/2773 days = or 14.328 days
Thus, Carol, Amanda, and Dorothy working together will finish the total work (1 work) in 14 910/2773 days = or 14.328 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Carol = 42 days
And the number of days required to finish the same work by Amanda = 43 days
And the number of days required to finish the work by Dorothy = 44 days
Thus, the number of days required to finish the work by Carol, Amanda, and Dorothy together = ?
Here a = 42 days
And, b = 43 days
And, c = 44 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Carol, Amanda, and Dorothy working together
= 42 × 43 × 44/42 × 43 + 42 × 44 + 43 × 44 days
= 79464/1806 + 1848 + 1892 days
= 79464/5546 days
= 79464/5546 days
= 79464 ÷ 2/5546 ÷ 2 = 39732/2773 days
= 14 910/2773 days or 14.328
Thus, Carol, Amanda, and Dorothy together will finish the work in 14 910/2773 days or 14.328 days Answer
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