Question:
Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?
Correct Answer
31 7261/26483 days or 31.274 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Gregory = 89 days
And, the number of days required to finish the same work by Frank = 94 days
And, the number of days required to finish the same work by Patrick = 99 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 89 days the work is done by Gregory = 1
∴ The work done by Gregory in 1 day = 1/89
Similarly,
∵ In 94 days the work is done by Frank = 1
∴ The work done by Frank in 1 day = 1/94
Similarly,
∵ In 99 days the work is done by Patrick = 1
∴ The work done by Patrick in 1 day = 1/99 part
Now, the work done by Gregory, Frank, and Patrick together in 1 day
= Gregory's 1 day work + Frank's 1 day work + Patrick's 1 day work
= 1/89 + 1/94 + 1/99
= 9306 + 8811 + 8366/828234
= 26483/828234 part of work
This means in 1 day, 26483/828234 part of work is done by Gregory, Frank and Patrick working together.
Now, the number of days required to finish 26483/828234 part of work by Gregory, Frank, and Patrick working together = 1
∴ the number of days required to finish the whole work (1 work) by Gregory + Frank + Patrick together
= 1/26483/828234
= 1 × 828234/26483 = 828234/26483 days
= 31 7261/26483 days = or 31.274 days
Thus, Gregory, Frank, and Patrick working together will finish the total work (1 work) in 31 7261/26483 days = or 31.274 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 Gregory = 89 days
And the number of days required to finish the same work by Frank = 94 days
And the number of days required to finish the work by Patrick = 99 days
Thus, the number of days required to finish the work by Gregory, Frank, and Patrick together = ?
Here a = 89 days
And, b = 94 days
And, c = 99 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Gregory, Frank, and Patrick working together
= 89 × 94 × 99/89 × 94 + 89 × 99 + 94 × 99 days
= 828234/8366 + 8811 + 9306 days
= 828234/26483 days
= 828234/26483 days
= 31 7261/26483 days or 31.274
Thus, Gregory, Frank, and Patrick together will finish the work in 31 7261/26483 days or 31.274 days Answer
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