Question:
Ashley can finish a work in 32 days. Kimberly can finish the same work in 33 days while Emily can finish the work in 34 days. How long will it take to finish it if they work together?
Correct Answer
10 1622/1633 days or 10.993 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Ashley = 32 days
And, the number of days required to finish the same work by Kimberly = 33 days
And, the number of days required to finish the same work by Emily = 34 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 32 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/32
Similarly,
∵ In 33 days the work is done by Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/33
Similarly,
∵ In 34 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/34 part
Now, the work done by Ashley, Kimberly, and Emily together in 1 day
= Ashley's 1 day work + Kimberly's 1 day work + Emily's 1 day work
= 1/32 + 1/33 + 1/34
= 561 + 544 + 528/17952
= 1633/17952 part of work
This means in 1 day, 1633/17952 part of work is done by Ashley, Kimberly and Emily working together.
Now, the number of days required to finish 1633/17952 part of work by Ashley, Kimberly, and Emily working together = 1
∴ the number of days required to finish the whole work (1 work) by Ashley + Kimberly + Emily together
= 1/1633/17952
= 1 × 17952/1633 = 17952/1633 days
= 10 1622/1633 days = or 10.993 days
Thus, Ashley, Kimberly, and Emily working together will finish the total work (1 work) in 10 1622/1633 days = or 10.993 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 Ashley = 32 days
And the number of days required to finish the same work by Kimberly = 33 days
And the number of days required to finish the work by Emily = 34 days
Thus, the number of days required to finish the work by Ashley, Kimberly, and Emily together = ?
Here a = 32 days
And, b = 33 days
And, c = 34 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Ashley, Kimberly, and Emily working together
= 32 × 33 × 34/32 × 33 + 32 × 34 + 33 × 34 days
= 35904/1056 + 1088 + 1122 days
= 35904/3266 days
= 35904/3266 days
= 35904 ÷ 2/3266 ÷ 2 = 17952/1633 days
= 10 1622/1633 days or 10.993
Thus, Ashley, Kimberly, and Emily together will finish the work in 10 1622/1633 days or 10.993 days Answer
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