Question:
Andrew can finish a work in 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?
Correct Answer
12 2862/4331 days or 12.661 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Andrew = 37 days
And, the number of days required to finish the same work by Joshua = 38 days
And, the number of days required to finish the same work by Kenneth = 39 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 37 days the work is done by Andrew = 1
∴ The work done by Andrew in 1 day = 1/37
Similarly,
∵ In 38 days the work is done by Joshua = 1
∴ The work done by Joshua in 1 day = 1/38
Similarly,
∵ In 39 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/39 part
Now, the work done by Andrew, Joshua, and Kenneth together in 1 day
= Andrew's 1 day work + Joshua's 1 day work + Kenneth's 1 day work
= 1/37 + 1/38 + 1/39
= 1482 + 1443 + 1406/54834
= 4331/54834 part of work
This means in 1 day, 4331/54834 part of work is done by Andrew, Joshua and Kenneth working together.
Now, the number of days required to finish 4331/54834 part of work by Andrew, Joshua, and Kenneth working together = 1
∴ the number of days required to finish the whole work (1 work) by Andrew + Joshua + Kenneth together
= 1/4331/54834
= 1 × 54834/4331 = 54834/4331 days
= 12 2862/4331 days = or 12.661 days
Thus, Andrew, Joshua, and Kenneth working together will finish the total work (1 work) in 12 2862/4331 days = or 12.661 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 Andrew = 37 days
And the number of days required to finish the same work by Joshua = 38 days
And the number of days required to finish the work by Kenneth = 39 days
Thus, the number of days required to finish the work by Andrew, Joshua, and Kenneth together = ?
Here a = 37 days
And, b = 38 days
And, c = 39 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Andrew, Joshua, and Kenneth working together
= 37 × 38 × 39/37 × 38 + 37 × 39 + 38 × 39 days
= 54834/1406 + 1443 + 1482 days
= 54834/4331 days
= 54834/4331 days
= 12 2862/4331 days or 12.661
Thus, Andrew, Joshua, and Kenneth together will finish the work in 12 2862/4331 days or 12.661 days Answer
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