Question : Kimberly can finish a work in 38 days. Donna can finish the same work in 43 days while Michelle can finish the work in 48 days. How long will it take to finish it if they work together?
Correct Answer 14 562/2761 days or 14.204 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Kimberly = 38 days
And, the number of days required to finish the same work by Donna = 43 days
And, the number of days required to finish the same work by Michelle = 48 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 Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/38
Similarly,
∵ In 43 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/43
Similarly,
∵ In 48 days the work is done by Michelle = 1
∴ The work done by Michelle in 1 day = 1/48 part
Now, the work done by Kimberly, Donna, and Michelle together in 1 day
= Kimberly's 1 day work + Donna's 1 day work + Michelle's 1 day work
= 1/38 + 1/43 + 1/48
= 1032 + 912 + 817/39216
= 2761/39216 part of work
This means in 1 day, 2761/39216 part of work is done by Kimberly, Donna and Michelle working together.
Now, the number of days required to finish 2761/39216 part of work by Kimberly, Donna, and Michelle working together = 1
∴ the number of days required to finish the whole work (1 work) by Kimberly + Donna + Michelle together
= 1/2761/39216
= 1 × 39216/2761 = 39216/2761 days
= 14 562/2761 days = or 14.204 days
Thus, Kimberly, Donna, and Michelle working together will finish the total work (1 work) in 14 562/2761 days = or 14.204 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 Kimberly = 38 days
And the number of days required to finish the same work by Donna = 43 days
And the number of days required to finish the work by Michelle = 48 days
Thus, the number of days required to finish the work by Kimberly, Donna, and Michelle together = ?
Here a = 38 days
And, b = 43 days
And, c = 48 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kimberly, Donna, and Michelle working together
= 38 × 43 × 48/38 × 43 + 38 × 48 + 43 × 48 days
= 78432/1634 + 1824 + 2064 days
= 78432/5522 days
= 78432/5522 days
= 78432 ÷ 2/5522 ÷ 2 = 39216/2761 days
= 14 562/2761 days or 14.204
Thus, Kimberly, Donna, and Michelle together will finish the work in 14 562/2761 days or 14.204 days Answer
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