Question:
Kimberly can finish a work in 34 days. Emily can finish the same work in 35 days while Donna can finish the work in 36 days. How long will it take to finish it if they work together?
Correct Answer
11 1213/1837 days or 11.66 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Kimberly = 34 days
And, the number of days required to finish the same work by Emily = 35 days
And, the number of days required to finish the same work by Donna = 36 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 34 days the work is done by Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/34
Similarly,
∵ In 35 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/35
Similarly,
∵ In 36 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/36 part
Now, the work done by Kimberly, Emily, and Donna together in 1 day
= Kimberly's 1 day work + Emily's 1 day work + Donna's 1 day work
= 1/34 + 1/35 + 1/36
= 630 + 612 + 595/21420
= 1837/21420 part of work
This means in 1 day, 1837/21420 part of work is done by Kimberly, Emily and Donna working together.
Now, the number of days required to finish 1837/21420 part of work by Kimberly, Emily, and Donna working together = 1
∴ the number of days required to finish the whole work (1 work) by Kimberly + Emily + Donna together
= 1/1837/21420
= 1 × 21420/1837 = 21420/1837 days
= 11 1213/1837 days = or 11.66 days
Thus, Kimberly, Emily, and Donna working together will finish the total work (1 work) in 11 1213/1837 days = or 11.66 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 = 34 days
And the number of days required to finish the same work by Emily = 35 days
And the number of days required to finish the work by Donna = 36 days
Thus, the number of days required to finish the work by Kimberly, Emily, and Donna together = ?
Here a = 34 days
And, b = 35 days
And, c = 36 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kimberly, Emily, and Donna working together
= 34 × 35 × 36/34 × 35 + 34 × 36 + 35 × 36 days
= 42840/1190 + 1224 + 1260 days
= 42840/3674 days
= 42840/3674 days
= 42840 ÷ 2/3674 ÷ 2 = 21420/1837 days
= 11 1213/1837 days or 11.66
Thus, Kimberly, Emily, and Donna together will finish the work in 11 1213/1837 days or 11.66 days Answer
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