Question : Ashley can finish a work in 36 days. Emily can finish the same work in 41 days while Donna can finish the work in 46 days. How long will it take to finish it if they work together?
Correct Answer 13 1331/2509 days or 13.53 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Ashley = 36 days
And, the number of days required to finish the same work by Emily = 41 days
And, the number of days required to finish the same work by Donna = 46 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 36 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/36
Similarly,
∵ In 41 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/41
Similarly,
∵ In 46 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/46 part
Now, the work done by Ashley, Emily, and Donna together in 1 day
= Ashley's 1 day work + Emily's 1 day work + Donna's 1 day work
= 1/36 + 1/41 + 1/46
= 943 + 828 + 738/33948
= 2509/33948 part of work
This means in 1 day, 2509/33948 part of work is done by Ashley, Emily and Donna working together.
Now, the number of days required to finish 2509/33948 part of work by Ashley, Emily, and Donna working together = 1
∴ the number of days required to finish the whole work (1 work) by Ashley + Emily + Donna together
= 1/2509/33948
= 1 × 33948/2509 = 33948/2509 days
= 13 1331/2509 days = or 13.53 days
Thus, Ashley, Emily, and Donna working together will finish the total work (1 work) in 13 1331/2509 days = or 13.53 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 = 36 days
And the number of days required to finish the same work by Emily = 41 days
And the number of days required to finish the work by Donna = 46 days
Thus, the number of days required to finish the work by Ashley, Emily, and Donna together = ?
Here a = 36 days
And, b = 41 days
And, c = 46 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Ashley, Emily, and Donna working together
= 36 × 41 × 46/36 × 41 + 36 × 46 + 41 × 46 days
= 67896/1476 + 1656 + 1886 days
= 67896/5018 days
= 67896/5018 days
= 67896 ÷ 2/5018 ÷ 2 = 33948/2509 days
= 13 1331/2509 days or 13.53
Thus, Ashley, Emily, and Donna together will finish the work in 13 1331/2509 days or 13.53 days Answer
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