Question:
Paul can finish a work in 39 days. Joshua can finish the same work in 44 days while Kenneth can finish the work in 49 days. How long will it take to finish it if they work together?
Correct Answer
14 3122/5783 days or 14.54 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Paul = 39 days
And, the number of days required to finish the same work by Joshua = 44 days
And, the number of days required to finish the same work by Kenneth = 49 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 39 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/39
Similarly,
∵ In 44 days the work is done by Joshua = 1
∴ The work done by Joshua in 1 day = 1/44
Similarly,
∵ In 49 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/49 part
Now, the work done by Paul, Joshua, and Kenneth together in 1 day
= Paul's 1 day work + Joshua's 1 day work + Kenneth's 1 day work
= 1/39 + 1/44 + 1/49
= 2156 + 1911 + 1716/84084
= 5783/84084 part of work
This means in 1 day, 5783/84084 part of work is done by Paul, Joshua and Kenneth working together.
Now, the number of days required to finish 5783/84084 part of work by Paul, Joshua, and Kenneth working together = 1
∴ the number of days required to finish the whole work (1 work) by Paul + Joshua + Kenneth together
= 1/5783/84084
= 1 × 84084/5783 = 84084/5783 days
= 14 3122/5783 days = or 14.54 days
Thus, Paul, Joshua, and Kenneth working together will finish the total work (1 work) in 14 3122/5783 days = or 14.54 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 Paul = 39 days
And the number of days required to finish the same work by Joshua = 44 days
And the number of days required to finish the work by Kenneth = 49 days
Thus, the number of days required to finish the work by Paul, Joshua, and Kenneth together = ?
Here a = 39 days
And, b = 44 days
And, c = 49 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Paul, Joshua, and Kenneth working together
= 39 × 44 × 49/39 × 44 + 39 × 49 + 44 × 49 days
= 84084/1716 + 1911 + 2156 days
= 84084/5783 days
= 84084/5783 days
= 14 3122/5783 days or 14.54
Thus, Paul, Joshua, and Kenneth together will finish the work in 14 3122/5783 days or 14.54 days Answer
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