Question : Michelle can finish a work in 44 days. Amanda can finish the same work in 49 days while Dorothy can finish the work in 54 days. How long will it take to finish it if they work together?
Correct Answer 16 788/3589 days or 16.22 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Michelle = 44 days
And, the number of days required to finish the same work by Amanda = 49 days
And, the number of days required to finish the same work by Dorothy = 54 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 44 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/44
Similarly,
∵ In 49 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/49
Similarly,
∵ In 54 days the work is done by Dorothy = 1
∴ The work done by Dorothy in 1 day = 1/54 part
Now, the work done by Michelle, Amanda, and Dorothy together in 1 day
= Michelle's 1 day work + Amanda's 1 day work + Dorothy's 1 day work
= 1/44 + 1/49 + 1/54
= 1323 + 1188 + 1078/58212
= 3589/58212 part of work
This means in 1 day, 3589/58212 part of work is done by Michelle, Amanda and Dorothy working together.
Now, the number of days required to finish 3589/58212 part of work by Michelle, Amanda, and Dorothy working together = 1
∴ the number of days required to finish the whole work (1 work) by Michelle + Amanda + Dorothy together
= 1/3589/58212
= 1 × 58212/3589 = 58212/3589 days
= 16 788/3589 days = or 16.22 days
Thus, Michelle, Amanda, and Dorothy working together will finish the total work (1 work) in 16 788/3589 days = or 16.22 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 Michelle = 44 days
And the number of days required to finish the same work by Amanda = 49 days
And the number of days required to finish the work by Dorothy = 54 days
Thus, the number of days required to finish the work by Michelle, Amanda, and Dorothy together = ?
Here a = 44 days
And, b = 49 days
And, c = 54 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Michelle, Amanda, and Dorothy working together
= 44 × 49 × 54/44 × 49 + 44 × 54 + 49 × 54 days
= 116424/2156 + 2376 + 2646 days
= 116424/7178 days
= 116424/7178 days
= 116424 ÷ 2/7178 ÷ 2 = 58212/3589 days
= 16 788/3589 days or 16.22
Thus, Michelle, Amanda, and Dorothy together will finish the work in 16 788/3589 days or 16.22 days Answer
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