Question : Shirley can finish a work in 72 days. Brenda can finish the same work in 77 days while Pamela can finish the work in 82 days. How long will it take to finish it if they work together?
Correct Answer 25 5279/8881 days or 25.594 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Shirley = 72 days
And, the number of days required to finish the same work by Brenda = 77 days
And, the number of days required to finish the same work by Pamela = 82 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 72 days the work is done by Shirley = 1
∴ The work done by Shirley in 1 day = 1/72
Similarly,
∵ In 77 days the work is done by Brenda = 1
∴ The work done by Brenda in 1 day = 1/77
Similarly,
∵ In 82 days the work is done by Pamela = 1
∴ The work done by Pamela in 1 day = 1/82 part
Now, the work done by Shirley, Brenda, and Pamela together in 1 day
= Shirley's 1 day work + Brenda's 1 day work + Pamela's 1 day work
= 1/72 + 1/77 + 1/82
= 3157 + 2952 + 2772/227304
= 8881/227304 part of work
This means in 1 day, 8881/227304 part of work is done by Shirley, Brenda and Pamela working together.
Now, the number of days required to finish 8881/227304 part of work by Shirley, Brenda, and Pamela working together = 1
∴ the number of days required to finish the whole work (1 work) by Shirley + Brenda + Pamela together
= 1/8881/227304
= 1 × 227304/8881 = 227304/8881 days
= 25 5279/8881 days = or 25.594 days
Thus, Shirley, Brenda, and Pamela working together will finish the total work (1 work) in 25 5279/8881 days = or 25.594 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 Shirley = 72 days
And the number of days required to finish the same work by Brenda = 77 days
And the number of days required to finish the work by Pamela = 82 days
Thus, the number of days required to finish the work by Shirley, Brenda, and Pamela together = ?
Here a = 72 days
And, b = 77 days
And, c = 82 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Shirley, Brenda, and Pamela working together
= 72 × 77 × 82/72 × 77 + 72 × 82 + 77 × 82 days
= 454608/5544 + 5904 + 6314 days
= 454608/17762 days
= 454608/17762 days
= 454608 ÷ 2/17762 ÷ 2 = 227304/8881 days
= 25 5279/8881 days or 25.594
Thus, Shirley, Brenda, and Pamela together will finish the work in 25 5279/8881 days or 25.594 days Answer
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