Question:
Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?
Correct Answer
9 831/1261 days or 9.659 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Margaret = 28 days
And, the number of days required to finish the same work by Sandra = 29 days
And, the number of days required to finish the same work by Ashley = 30 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 28 days the work is done by Margaret = 1
∴ The work done by Margaret in 1 day = 1/28
Similarly,
∵ In 29 days the work is done by Sandra = 1
∴ The work done by Sandra in 1 day = 1/29
Similarly,
∵ In 30 days the work is done by Ashley = 1
∴ The work done by Ashley in 1 day = 1/30 part
Now, the work done by Margaret, Sandra, and Ashley together in 1 day
= Margaret's 1 day work + Sandra's 1 day work + Ashley's 1 day work
= 1/28 + 1/29 + 1/30
= 435 + 420 + 406/12180
= 1261/12180 part of work
This means in 1 day, 1261/12180 part of work is done by Margaret, Sandra and Ashley working together.
Now, the number of days required to finish 1261/12180 part of work by Margaret, Sandra, and Ashley working together = 1
∴ the number of days required to finish the whole work (1 work) by Margaret + Sandra + Ashley together
= 1/1261/12180
= 1 × 12180/1261 = 12180/1261 days
= 9 831/1261 days = or 9.659 days
Thus, Margaret, Sandra, and Ashley working together will finish the total work (1 work) in 9 831/1261 days = or 9.659 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 Margaret = 28 days
And the number of days required to finish the same work by Sandra = 29 days
And the number of days required to finish the work by Ashley = 30 days
Thus, the number of days required to finish the work by Margaret, Sandra, and Ashley together = ?
Here a = 28 days
And, b = 29 days
And, c = 30 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Margaret, Sandra, and Ashley working together
= 28 × 29 × 30/28 × 29 + 28 × 30 + 29 × 30 days
= 24360/812 + 840 + 870 days
= 24360/2522 days
= 24360/2522 days
= 24360 ÷ 2/2522 ÷ 2 = 12180/1261 days
= 9 831/1261 days or 9.659
Thus, Margaret, Sandra, and Ashley together will finish the work in 9 831/1261 days or 9.659 days Answer
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