Question:
Kenneth can finish a work in 41 days. Kevin can finish the same work in 42 days while Brian can finish the work in 43 days. How long will it take to finish it if they work together?
Correct Answer
13 5263/5291 days or 13.995 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Kenneth = 41 days
And, the number of days required to finish the same work by Kevin = 42 days
And, the number of days required to finish the same work by Brian = 43 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 41 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/41
Similarly,
∵ In 42 days the work is done by Kevin = 1
∴ The work done by Kevin in 1 day = 1/42
Similarly,
∵ In 43 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/43 part
Now, the work done by Kenneth, Kevin, and Brian together in 1 day
= Kenneth's 1 day work + Kevin's 1 day work + Brian's 1 day work
= 1/41 + 1/42 + 1/43
= 1806 + 1763 + 1722/74046
= 5291/74046 part of work
This means in 1 day, 5291/74046 part of work is done by Kenneth, Kevin and Brian working together.
Now, the number of days required to finish 5291/74046 part of work by Kenneth, Kevin, and Brian working together = 1
∴ the number of days required to finish the whole work (1 work) by Kenneth + Kevin + Brian together
= 1/5291/74046
= 1 × 74046/5291 = 74046/5291 days
= 13 5263/5291 days = or 13.995 days
Thus, Kenneth, Kevin, and Brian working together will finish the total work (1 work) in 13 5263/5291 days = or 13.995 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 Kenneth = 41 days
And the number of days required to finish the same work by Kevin = 42 days
And the number of days required to finish the work by Brian = 43 days
Thus, the number of days required to finish the work by Kenneth, Kevin, and Brian together = ?
Here a = 41 days
And, b = 42 days
And, c = 43 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kenneth, Kevin, and Brian working together
= 41 × 42 × 43/41 × 42 + 41 × 43 + 42 × 43 days
= 74046/1722 + 1763 + 1806 days
= 74046/5291 days
= 74046/5291 days
= 13 5263/5291 days or 13.995
Thus, Kenneth, Kevin, and Brian together will finish the work in 13 5263/5291 days or 13.995 days Answer
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