Question:
Joshua can finish a work in 39 days. Kenneth can finish the same work in 40 days while Kevin can finish the work in 41 days. How long will it take to finish it if they work together?
Correct Answer
13 1573/4799 days or 13.328 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Joshua = 39 days
And, the number of days required to finish the same work by Kenneth = 40 days
And, the number of days required to finish the same work by Kevin = 41 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 Joshua = 1
∴ The work done by Joshua in 1 day = 1/39
Similarly,
∵ In 40 days the work is done by Kenneth = 1
∴ The work done by Kenneth in 1 day = 1/40
Similarly,
∵ In 41 days the work is done by Kevin = 1
∴ The work done by Kevin in 1 day = 1/41 part
Now, the work done by Joshua, Kenneth, and Kevin together in 1 day
= Joshua's 1 day work + Kenneth's 1 day work + Kevin's 1 day work
= 1/39 + 1/40 + 1/41
= 1640 + 1599 + 1560/63960
= 4799/63960 part of work
This means in 1 day, 4799/63960 part of work is done by Joshua, Kenneth and Kevin working together.
Now, the number of days required to finish 4799/63960 part of work by Joshua, Kenneth, and Kevin working together = 1
∴ the number of days required to finish the whole work (1 work) by Joshua + Kenneth + Kevin together
= 1/4799/63960
= 1 × 63960/4799 = 63960/4799 days
= 13 1573/4799 days = or 13.328 days
Thus, Joshua, Kenneth, and Kevin working together will finish the total work (1 work) in 13 1573/4799 days = or 13.328 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 Joshua = 39 days
And the number of days required to finish the same work by Kenneth = 40 days
And the number of days required to finish the work by Kevin = 41 days
Thus, the number of days required to finish the work by Joshua, Kenneth, and Kevin together = ?
Here a = 39 days
And, b = 40 days
And, c = 41 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Joshua, Kenneth, and Kevin working together
= 39 × 40 × 41/39 × 40 + 39 × 41 + 40 × 41 days
= 63960/1560 + 1599 + 1640 days
= 63960/4799 days
= 63960/4799 days
= 13 1573/4799 days or 13.328
Thus, Joshua, Kenneth, and Kevin together will finish the work in 13 1573/4799 days or 13.328 days Answer
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