Question:
Kevin can finish a work in 43 days. Brian can finish the same work in 44 days while George can finish the work in 45 days. How long will it take to finish it if they work together?
Correct Answer
14 3842/5807 days or 14.662 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Kevin = 43 days
And, the number of days required to finish the same work by Brian = 44 days
And, the number of days required to finish the same work by George = 45 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 43 days the work is done by Kevin = 1
∴ The work done by Kevin in 1 day = 1/43
Similarly,
∵ In 44 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/44
Similarly,
∵ In 45 days the work is done by George = 1
∴ The work done by George in 1 day = 1/45 part
Now, the work done by Kevin, Brian, and George together in 1 day
= Kevin's 1 day work + Brian's 1 day work + George's 1 day work
= 1/43 + 1/44 + 1/45
= 1980 + 1935 + 1892/85140
= 5807/85140 part of work
This means in 1 day, 5807/85140 part of work is done by Kevin, Brian and George working together.
Now, the number of days required to finish 5807/85140 part of work by Kevin, Brian, and George working together = 1
∴ the number of days required to finish the whole work (1 work) by Kevin + Brian + George together
= 1/5807/85140
= 1 × 85140/5807 = 85140/5807 days
= 14 3842/5807 days = or 14.662 days
Thus, Kevin, Brian, and George working together will finish the total work (1 work) in 14 3842/5807 days = or 14.662 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 Kevin = 43 days
And the number of days required to finish the same work by Brian = 44 days
And the number of days required to finish the work by George = 45 days
Thus, the number of days required to finish the work by Kevin, Brian, and George together = ?
Here a = 43 days
And, b = 44 days
And, c = 45 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kevin, Brian, and George working together
= 43 × 44 × 45/43 × 44 + 43 × 45 + 44 × 45 days
= 85140/1892 + 1935 + 1980 days
= 85140/5807 days
= 85140/5807 days
= 14 3842/5807 days or 14.662
Thus, Kevin, Brian, and George together will finish the work in 14 3842/5807 days or 14.662 days Answer
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