Question : Donna can finish a work in 38 days. Michelle can finish the same work in 39 days while Carol can finish the work in 40 days. How long will it take to finish it if they work together?
Correct Answer 12 2268/2281 days or 12.994 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Donna = 38 days
And, the number of days required to finish the same work by Michelle = 39 days
And, the number of days required to finish the same work by Carol = 40 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 38 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/38
Similarly,
∵ In 39 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/39
Similarly,
∵ In 40 days the work is done by Carol = 1
∴ The work done by Carol in 1 day = 1/40 part
Now, the work done by Donna, Michelle, and Carol together in 1 day
= Donna's 1 day work + Michelle's 1 day work + Carol's 1 day work
= 1/38 + 1/39 + 1/40
= 780 + 760 + 741/29640
= 2281/29640 part of work
This means in 1 day, 2281/29640 part of work is done by Donna, Michelle and Carol working together.
Now, the number of days required to finish 2281/29640 part of work by Donna, Michelle, and Carol working together = 1
∴ the number of days required to finish the whole work (1 work) by Donna + Michelle + Carol together
= 1/2281/29640
= 1 × 29640/2281 = 29640/2281 days
= 12 2268/2281 days = or 12.994 days
Thus, Donna, Michelle, and Carol working together will finish the total work (1 work) in 12 2268/2281 days = or 12.994 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 Donna = 38 days
And the number of days required to finish the same work by Michelle = 39 days
And the number of days required to finish the work by Carol = 40 days
Thus, the number of days required to finish the work by Donna, Michelle, and Carol together = ?
Here a = 38 days
And, b = 39 days
And, c = 40 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Donna, Michelle, and Carol working together
= 38 × 39 × 40/38 × 39 + 38 × 40 + 39 × 40 days
= 59280/1482 + 1520 + 1560 days
= 59280/4562 days
= 59280/4562 days
= 59280 ÷ 2/4562 ÷ 2 = 29640/2281 days
= 12 2268/2281 days or 12.994
Thus, Donna, Michelle, and Carol together will finish the work in 12 2268/2281 days or 12.994 days Answer
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