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 And 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
Similar Questions
(1) If Margaret can finish the work in 29 days and Ryan can finish the same work in 33 days, then in how many days both can finish the work together?
(2) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?
(3) Janet can finish a work in 98 days. Maria can finish the same work in 103 days while Heather can finish the work in 108 days. How long will it take to finish it if they work together?
(4) If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?
(5) If Richard can finish the work in 17 days and Mark can finish the same work in 22 days, then in how many days both can finish the work together?
(6) Timothy can finish a work in 53 days. Edward can finish the same work in 58 days while Jason can finish the work in 63 days. How long will it take to finish it if they work together?
(7) Cynthia can finish a work in 64 days. Amy can finish the same work in 69 days while Angela can finish the work in 74 days. How long will it take to finish it if they work together?
(8) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?
(9) If Joshua can finish the work in 40 days and Benjamin can finish the same work in 43 days, then in how many days both can finish the work together?
(10) Brian can finish a work in 45 days. George can finish the same work in 46 days while Timothy can finish the work in 47 days. How long will it take to finish it if they work together?