Question : Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?
Correct Answer 30 3378/12409 days or 30.272 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Samantha = 86 days
And, the number of days required to finish the same work by Christine = 91 days
And, the number of days required to finish the same work by Debra = 96 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 86 days the work is done by Samantha = 1
∴ The work done by Samantha in 1 day = 1/86
Similarly,
∵ In 91 days the work is done by Christine = 1
∴ The work done by Christine in 1 day = 1/91
Similarly,
∵ In 96 days the work is done by Debra = 1
∴ The work done by Debra in 1 day = 1/96 part
Now, the work done by Samantha, Christine, and Debra together in 1 day
= Samantha's 1 day work + Christine's 1 day work + Debra's 1 day work
= 1/86 + 1/91 + 1/96
= 4368 + 4128 + 3913/375648
= 12409/375648 part of work
This means in 1 day, 12409/375648 part of work is done by Samantha, Christine and Debra working together.
Now, the number of days required to finish 12409/375648 part of work by Samantha, Christine, and Debra working together = 1
∴ the number of days required to finish the whole work (1 work) by Samantha + Christine + Debra together
= 1/12409/375648
= 1 × 375648/12409 = 375648/12409 days
= 30 3378/12409 days = or 30.272 days
Thus, Samantha, Christine, and Debra working together will finish the total work (1 work) in 30 3378/12409 days = or 30.272 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 Samantha = 86 days
And the number of days required to finish the same work by Christine = 91 days
And the number of days required to finish the work by Debra = 96 days
Thus, the number of days required to finish the work by Samantha, Christine, and Debra together = ?
Here a = 86 days
And, b = 91 days
And, c = 96 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Samantha, Christine, and Debra working together
= 86 × 91 × 96/86 × 91 + 86 × 96 + 91 × 96 days
= 751296/7826 + 8256 + 8736 days
= 751296/24818 days
= 751296/24818 days
= 751296 ÷ 2/24818 ÷ 2 = 375648/12409 days
= 30 3378/12409 days or 30.272
Thus, Samantha, Christine, and Debra together will finish the work in 30 3378/12409 days or 30.272 days Answer
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