Question : Deborah can finish a work in 54 days. Rebecca can finish the same work in 59 days while Sharon can finish the work in 64 days. How long will it take to finish it if they work together?
Correct Answer 19 2981/5209 days or 19.572 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Deborah = 54 days
And, the number of days required to finish the same work by Rebecca = 59 days
And, the number of days required to finish the same work by Sharon = 64 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 54 days the work is done by Deborah = 1
∴ The work done by Deborah in 1 day = 1/54
Similarly,
∵ In 59 days the work is done by Rebecca = 1
∴ The work done by Rebecca in 1 day = 1/59
Similarly,
∵ In 64 days the work is done by Sharon = 1
∴ The work done by Sharon in 1 day = 1/64 part
Now, the work done by Deborah, Rebecca, and Sharon together in 1 day
= Deborah's 1 day work + Rebecca's 1 day work + Sharon's 1 day work
= 1/54 + 1/59 + 1/64
= 1888 + 1728 + 1593/101952
= 5209/101952 part of work
This means in 1 day, 5209/101952 part of work is done by Deborah, Rebecca and Sharon working together.
Now, the number of days required to finish 5209/101952 part of work by Deborah, Rebecca, and Sharon working together = 1
∴ the number of days required to finish the whole work (1 work) by Deborah + Rebecca + Sharon together
= 1/5209/101952
= 1 × 101952/5209 = 101952/5209 days
= 19 2981/5209 days = or 19.572 days
Thus, Deborah, Rebecca, and Sharon working together will finish the total work (1 work) in 19 2981/5209 days = or 19.572 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 Deborah = 54 days
And the number of days required to finish the same work by Rebecca = 59 days
And the number of days required to finish the work by Sharon = 64 days
Thus, the number of days required to finish the work by Deborah, Rebecca, and Sharon together = ?
Here a = 54 days
And, b = 59 days
And, c = 64 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Deborah, Rebecca, and Sharon working together
= 54 × 59 × 64/54 × 59 + 54 × 64 + 59 × 64 days
= 203904/3186 + 3456 + 3776 days
= 203904/10418 days
= 203904/10418 days
= 203904 ÷ 2/10418 ÷ 2 = 101952/5209 days
= 19 2981/5209 days or 19.572
Thus, Deborah, Rebecca, and Sharon together will finish the work in 19 2981/5209 days or 19.572 days Answer
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