Question:
Brenda can finish a work in 76 days. Emma can finish the same work in 81 days while Nicole can finish the work in 86 days. How long will it take to finish it if they work together?
Correct Answer
26 9154/9829 days or 26.931 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Brenda = 76 days
And, the number of days required to finish the same work by Emma = 81 days
And, the number of days required to finish the same work by Nicole = 86 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 76 days the work is done by Brenda = 1
∴ The work done by Brenda in 1 day = 1/76
Similarly,
∵ In 81 days the work is done by Emma = 1
∴ The work done by Emma in 1 day = 1/81
Similarly,
∵ In 86 days the work is done by Nicole = 1
∴ The work done by Nicole in 1 day = 1/86 part
Now, the work done by Brenda, Emma, and Nicole together in 1 day
= Brenda's 1 day work + Emma's 1 day work + Nicole's 1 day work
= 1/76 + 1/81 + 1/86
= 3483 + 3268 + 3078/264708
= 9829/264708 part of work
This means in 1 day, 9829/264708 part of work is done by Brenda, Emma and Nicole working together.
Now, the number of days required to finish 9829/264708 part of work by Brenda, Emma, and Nicole working together = 1
∴ the number of days required to finish the whole work (1 work) by Brenda + Emma + Nicole together
= 1/9829/264708
= 1 × 264708/9829 = 264708/9829 days
= 26 9154/9829 days = or 26.931 days
Thus, Brenda, Emma, and Nicole working together will finish the total work (1 work) in 26 9154/9829 days = or 26.931 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 Brenda = 76 days
And the number of days required to finish the same work by Emma = 81 days
And the number of days required to finish the work by Nicole = 86 days
Thus, the number of days required to finish the work by Brenda, Emma, and Nicole together = ?
Here a = 76 days
And, b = 81 days
And, c = 86 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Brenda, Emma, and Nicole working together
= 76 × 81 × 86/76 × 81 + 76 × 86 + 81 × 86 days
= 529416/6156 + 6536 + 6966 days
= 529416/19658 days
= 529416/19658 days
= 529416 ÷ 2/19658 ÷ 2 = 264708/9829 days
= 26 9154/9829 days or 26.931
Thus, Brenda, Emma, and Nicole together will finish the work in 26 9154/9829 days or 26.931 days Answer
Similar Questions
(1) If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?
(2) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work 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 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?
(5) David can finish a work in 13 days. Richard can finish the same work in 18 days while Joseph can finish the work in 23 days. How long will it take to finish it if they work together?
(6) If Sarah can finish the work in 19 days and Joshua can finish the same work in 22 days, then in how many days both can finish the work together?
(7) Sandra can finish a work in 30 days. Ashley can finish the same work in 31 days while Kimberly can finish the work in 32 days. How long will it take to finish it if they work together?
(8) Mary can finish a work in 6 days. Jennifer can finish the same work in 11 days while Linda can finish the work in 16 days. How long will it take to finish it if they work together?
(9) If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?
(10) Sarah can finish a work in 18 days. Karen can finish the same work in 19 days while Lisa can finish the work in 20 days. How long will it take to finish it if they work together?