Question:
Cynthia can finish a work in 64 days. Amy can finish the same work in 69 days while Angela can finish the work in 74 days. How long will it take to finish it if they work together?
Correct Answer
22 6554/7129 days or 22.919 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Cynthia = 64 days
And, the number of days required to finish the same work by Amy = 69 days
And, the number of days required to finish the same work by Angela = 74 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 64 days the work is done by Cynthia = 1
∴ The work done by Cynthia in 1 day = 1/64
Similarly,
∵ In 69 days the work is done by Amy = 1
∴ The work done by Amy in 1 day = 1/69
Similarly,
∵ In 74 days the work is done by Angela = 1
∴ The work done by Angela in 1 day = 1/74 part
Now, the work done by Cynthia, Amy, and Angela together in 1 day
= Cynthia's 1 day work + Amy's 1 day work + Angela's 1 day work
= 1/64 + 1/69 + 1/74
= 2553 + 2368 + 2208/163392
= 7129/163392 part of work
This means in 1 day, 7129/163392 part of work is done by Cynthia, Amy and Angela working together.
Now, the number of days required to finish 7129/163392 part of work by Cynthia, Amy, and Angela working together = 1
∴ the number of days required to finish the whole work (1 work) by Cynthia + Amy + Angela together
= 1/7129/163392
= 1 × 163392/7129 = 163392/7129 days
= 22 6554/7129 days = or 22.919 days
Thus, Cynthia, Amy, and Angela working together will finish the total work (1 work) in 22 6554/7129 days = or 22.919 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 Cynthia = 64 days
And the number of days required to finish the same work by Amy = 69 days
And the number of days required to finish the work by Angela = 74 days
Thus, the number of days required to finish the work by Cynthia, Amy, and Angela together = ?
Here a = 64 days
And, b = 69 days
And, c = 74 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Cynthia, Amy, and Angela working together
= 64 × 69 × 74/64 × 69 + 64 × 74 + 69 × 74 days
= 326784/4416 + 4736 + 5106 days
= 326784/14258 days
= 326784/14258 days
= 326784 ÷ 2/14258 ÷ 2 = 163392/7129 days
= 22 6554/7129 days or 22.919
Thus, Cynthia, Amy, and Angela together will finish the work in 22 6554/7129 days or 22.919 days Answer
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