Question:
Kathleen can finish a work in 66 days. Angela can finish the same work in 71 days while Shirley can finish the work in 76 days. How long will it take to finish it if they work together?
Correct Answer
23 4441/7549 days or 23.588 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Kathleen = 66 days
And, the number of days required to finish the same work by Angela = 71 days
And, the number of days required to finish the same work by Shirley = 76 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 66 days the work is done by Kathleen = 1
∴ The work done by Kathleen in 1 day = 1/66
Similarly,
∵ In 71 days the work is done by Angela = 1
∴ The work done by Angela in 1 day = 1/71
Similarly,
∵ In 76 days the work is done by Shirley = 1
∴ The work done by Shirley in 1 day = 1/76 part
Now, the work done by Kathleen, Angela, and Shirley together in 1 day
= Kathleen's 1 day work + Angela's 1 day work + Shirley's 1 day work
= 1/66 + 1/71 + 1/76
= 2698 + 2508 + 2343/178068
= 7549/178068 part of work
This means in 1 day, 7549/178068 part of work is done by Kathleen, Angela and Shirley working together.
Now, the number of days required to finish 7549/178068 part of work by Kathleen, Angela, and Shirley working together = 1
∴ the number of days required to finish the whole work (1 work) by Kathleen + Angela + Shirley together
= 1/7549/178068
= 1 × 178068/7549 = 178068/7549 days
= 23 4441/7549 days = or 23.588 days
Thus, Kathleen, Angela, and Shirley working together will finish the total work (1 work) in 23 4441/7549 days = or 23.588 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 Kathleen = 66 days
And the number of days required to finish the same work by Angela = 71 days
And the number of days required to finish the work by Shirley = 76 days
Thus, the number of days required to finish the work by Kathleen, Angela, and Shirley together = ?
Here a = 66 days
And, b = 71 days
And, c = 76 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kathleen, Angela, and Shirley working together
= 66 × 71 × 76/66 × 71 + 66 × 76 + 71 × 76 days
= 356136/4686 + 5016 + 5396 days
= 356136/15098 days
= 356136/15098 days
= 356136 ÷ 2/15098 ÷ 2 = 178068/7549 days
= 23 4441/7549 days or 23.588
Thus, Kathleen, Angela, and Shirley together will finish the work in 23 4441/7549 days or 23.588 days Answer
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