Question : Sharon can finish a work in 60 days. Cynthia can finish the same work in 65 days while Kathleen can finish the work in 70 days. How long will it take to finish it if they work together?
Correct Answer 21 147/253 days or 21.581 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Sharon = 60 days
And, the number of days required to finish the same work by Cynthia = 65 days
And, the number of days required to finish the same work by Kathleen = 70 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 60 days the work is done by Sharon = 1
∴ The work done by Sharon in 1 day = 1/60
Similarly,
∵ In 65 days the work is done by Cynthia = 1
∴ The work done by Cynthia in 1 day = 1/65
Similarly,
∵ In 70 days the work is done by Kathleen = 1
∴ The work done by Kathleen in 1 day = 1/70 part
Now, the work done by Sharon, Cynthia, and Kathleen together in 1 day
= Sharon's 1 day work + Cynthia's 1 day work + Kathleen's 1 day work
= 1/60 + 1/65 + 1/70
= 91 + 84 + 78/5460
= 253/5460 part of work
This means in 1 day, 253/5460 part of work is done by Sharon, Cynthia and Kathleen working together.
Now, the number of days required to finish 253/5460 part of work by Sharon, Cynthia, and Kathleen working together = 1
∴ the number of days required to finish the whole work (1 work) by Sharon + Cynthia + Kathleen together
= 1/253/5460
= 1 × 5460/253 = 5460/253 days
= 21 147/253 days = or 21.581 days
Thus, Sharon, Cynthia, and Kathleen working together will finish the total work (1 work) in 21 147/253 days = or 21.581 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 Sharon = 60 days
And the number of days required to finish the same work by Cynthia = 65 days
And the number of days required to finish the work by Kathleen = 70 days
Thus, the number of days required to finish the work by Sharon, Cynthia, and Kathleen together = ?
Here a = 60 days
And, b = 65 days
And, c = 70 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Sharon, Cynthia, and Kathleen working together
= 60 × 65 × 70/60 × 65 + 60 × 70 + 65 × 70 days
= 273000/3900 + 4200 + 4550 days
= 273000/12650 days
= 273000/12650 days
= 273000 ÷ 50/12650 ÷ 50 = 5460/253 days
= 21 147/253 days or 21.581
Thus, Sharon, Cynthia, and Kathleen together will finish the work in 21 147/253 days or 21.581 days Answer
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