Question:
Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?
Correct Answer
4 724/743 days or 4.974 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Michael = 11 days
And, the number of days required to finish the same work by William = 16 days
And, the number of days required to finish the same work by Richard = 21 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 11 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/11
Similarly,
∵ In 16 days the work is done by William = 1
∴ The work done by William in 1 day = 1/16
Similarly,
∵ In 21 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/21 part
Now, the work done by Michael, William, and Richard together in 1 day
= Michael's 1 day work + William's 1 day work + Richard's 1 day work
= 1/11 + 1/16 + 1/21
= 336 + 231 + 176/3696
= 743/3696 part of work
This means in 1 day, 743/3696 part of work is done by Michael, William and Richard working together.
Now, the number of days required to finish 743/3696 part of work by Michael, William, and Richard working together = 1
∴ the number of days required to finish the whole work (1 work) by Michael + William + Richard together
= 1/743/3696
= 1 × 3696/743 = 3696/743 days
= 4 724/743 days = or 4.974 days
Thus, Michael, William, and Richard working together will finish the total work (1 work) in 4 724/743 days = or 4.974 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 Michael = 11 days
And the number of days required to finish the same work by William = 16 days
And the number of days required to finish the work by Richard = 21 days
Thus, the number of days required to finish the work by Michael, William, and Richard together = ?
Here a = 11 days
And, b = 16 days
And, c = 21 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Michael, William, and Richard working together
= 11 × 16 × 21/11 × 16 + 11 × 21 + 16 × 21 days
= 3696/176 + 231 + 336 days
= 3696/743 days
= 3696/743 days
= 4 724/743 days or 4.974
Thus, Michael, William, and Richard together will finish the work in 4 724/743 days or 4.974 days Answer
Similar Questions
(1) If Kenneth can finish the work in 45 days and Gregory can finish the same work in 50 days, then in how many days both can finish the work together?
(2) Daniel can finish a work in 27 days. Anthony can finish the same work in 32 days while Mark can finish the work in 37 days. How long will it take to finish it if they work together?
(3) If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?
(4) Jennifer can finish a work in 6 days. Linda can finish the same work in 7 days while Elizabeth can finish the work in 8 days. How long will it take to finish it if they work together?
(5) If David can finish the work in 10 days and Christopher can finish the same work in 14 days, then in how many days both can finish the work together?
(6) If Richard can finish the work in 14 days and Mark can finish the same work in 18 days, then in how many days both can finish the work together?
(7) Kimberly can finish a work in 38 days. Donna can finish the same work in 43 days while Michelle can finish the work in 48 days. How long will it take to finish it if they work together?
(8) If Donna can finish the work in 39 days and Brandon can finish the same work in 42 days, then in how many days both can finish the work together?
(9) Samuel can finish a work in 87 days. Alexander can finish the same work in 92 days while Frank can finish the work in 97 days. How long will it take to finish it if they work together?
(10) 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?