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
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