Question:
Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?
Correct Answer
1 13/47 days or 1.277 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Robert = 3 days
And, the number of days required to finish the same work by John = 4 days
And, the number of days required to finish the same work by Michael = 5 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 3 days the work is done by Robert = 1
∴ The work done by Robert in 1 day = 1/3
Similarly,
∵ In 4 days the work is done by John = 1
∴ The work done by John in 1 day = 1/4
Similarly,
∵ In 5 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/5 part
Now, the work done by Robert, John, and Michael together in 1 day
= Robert's 1 day work + John's 1 day work + Michael's 1 day work
= 1/3 + 1/4 + 1/5
= 20 + 15 + 12/60
= 47/60 part of work
This means in 1 day, 47/60 part of work is done by Robert, John and Michael working together.
Now, the number of days required to finish 47/60 part of work by Robert, John, and Michael working together = 1
∴ the number of days required to finish the whole work (1 work) by Robert + John + Michael together
= 1/47/60
= 1 × 60/47 = 60/47 days
= 1 13/47 days = or 1.277 days
Thus, Robert, John, and Michael working together will finish the total work (1 work) in 1 13/47 days = or 1.277 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 Robert = 3 days
And the number of days required to finish the same work by John = 4 days
And the number of days required to finish the work by Michael = 5 days
Thus, the number of days required to finish the work by Robert, John, and Michael together = ?
Here a = 3 days
And, b = 4 days
And, c = 5 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Robert, John, and Michael working together
= 3 × 4 × 5/3 × 4 + 3 × 5 + 4 × 5 days
= 60/12 + 15 + 20 days
= 60/47 days
= 60/47 days
= 1 13/47 days or 1.277
Thus, Robert, John, and Michael together will finish the work in 1 13/47 days or 1.277 days Answer
Similar Questions
(1) If Stephanie can finish the work in 56 days and Adam can finish the same work in 61 days, then in how many days both can finish the work together?
(2) If Annie can finish a work in 2 days and Bobby can finish the same work in 3 days, then in how many days they both can finish the work working together?
(3) If Michael can finish the work in 8 days and Thomas can finish the same work in 11 days, then in how many days both can finish the work together?
(4) Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?
(5) Christopher can finish a work in 21 days. Daniel can finish the same work in 22 days while Matthew can finish the work in 23 days. How long will it take to finish it if they work together?
(6) Timothy can finish a work in 49 days. Ronald can finish the same work in 50 days while Edward can finish the work in 51 days. How long will it take to finish it if they work together?
(7) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?
(8) Lisa can finish a work in 22 days. Nancy can finish the same work in 23 days while Betty can finish the work in 24 days. How long will it take to finish it if they work together?
(9) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?
(10) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?