Question : Joshua can finish a work in 43 days. Kevin can finish the same work in 48 days while Brian can finish the work in 53 days. How long will it take to finish it if they work together?
Correct Answer 15 6087/6887 days or 15.884 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Joshua = 43 days
And, the number of days required to finish the same work by Kevin = 48 days
And, the number of days required to finish the same work by Brian = 53 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 Joshua = 1
∴ The work done by Joshua in 1 day = 1/43
Similarly,
∵ In 48 days the work is done by Kevin = 1
∴ The work done by Kevin in 1 day = 1/48
Similarly,
∵ In 53 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/53 part
Now, the work done by Joshua, Kevin, and Brian together in 1 day
= Joshua's 1 day work + Kevin's 1 day work + Brian's 1 day work
= 1/43 + 1/48 + 1/53
= 2544 + 2279 + 2064/109392
= 6887/109392 part of work
This means in 1 day, 6887/109392 part of work is done by Joshua, Kevin and Brian working together.
Now, the number of days required to finish 6887/109392 part of work by Joshua, Kevin, and Brian working together = 1
∴ the number of days required to finish the whole work (1 work) by Joshua + Kevin + Brian together
= 1/6887/109392
= 1 × 109392/6887 = 109392/6887 days
= 15 6087/6887 days = or 15.884 days
Thus, Joshua, Kevin, and Brian working together will finish the total work (1 work) in 15 6087/6887 days = or 15.884 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 = 43 days
And the number of days required to finish the same work by Kevin = 48 days
And the number of days required to finish the work by Brian = 53 days
Thus, the number of days required to finish the work by Joshua, Kevin, and Brian together = ?
Here a = 43 days
And, b = 48 days
And, c = 53 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Joshua, Kevin, and Brian working together
= 43 × 48 × 53/43 × 48 + 43 × 53 + 48 × 53 days
= 109392/2064 + 2279 + 2544 days
= 109392/6887 days
= 109392/6887 days
= 15 6087/6887 days or 15.884
Thus, Joshua, Kevin, and Brian together will finish the work in 15 6087/6887 days or 15.884 days Answer
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