Question : Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?
Correct Answer 12 1944/2269 days or 12.857 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Sandra = 34 days
And, the number of days required to finish the same work by Kimberly = 39 days
And, the number of days required to finish the same work by Emily = 44 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 Sandra = 1
∴ The work done by Sandra in 1 day = 1/34
Similarly,
∵ In 39 days the work is done by Kimberly = 1
∴ The work done by Kimberly in 1 day = 1/39
Similarly,
∵ In 44 days the work is done by Emily = 1
∴ The work done by Emily in 1 day = 1/44 part
Now, the work done by Sandra, Kimberly, and Emily together in 1 day
= Sandra's 1 day work + Kimberly's 1 day work + Emily's 1 day work
= 1/34 + 1/39 + 1/44
= 858 + 748 + 663/29172
= 2269/29172 part of work
This means in 1 day, 2269/29172 part of work is done by Sandra, Kimberly and Emily working together.
Now, the number of days required to finish 2269/29172 part of work by Sandra, Kimberly, and Emily working together = 1
∴ the number of days required to finish the whole work (1 work) by Sandra + Kimberly + Emily together
= 1/2269/29172
= 1 × 29172/2269 = 29172/2269 days
= 12 1944/2269 days = or 12.857 days
Thus, Sandra, Kimberly, and Emily working together will finish the total work (1 work) in 12 1944/2269 days = or 12.857 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 Sandra = 34 days
And the number of days required to finish the same work by Kimberly = 39 days
And the number of days required to finish the work by Emily = 44 days
Thus, the number of days required to finish the work by Sandra, Kimberly, and Emily together = ?
Here a = 34 days
And, b = 39 days
And, c = 44 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Sandra, Kimberly, and Emily working together
= 34 × 39 × 44/34 × 39 + 34 × 44 + 39 × 44 days
= 58344/1326 + 1496 + 1716 days
= 58344/4538 days
= 58344/4538 days
= 58344 ÷ 2/4538 ÷ 2 = 29172/2269 days
= 12 1944/2269 days or 12.857
Thus, Sandra, Kimberly, and Emily together will finish the work in 12 1944/2269 days or 12.857 days Answer
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