Question : Jonathan can finish a work in 73 days. Larry can finish the same work in 78 days while Justin can finish the work in 83 days. How long will it take to finish it if they work together?
Correct Answer 25 16927/18227 days or 25.929 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Jonathan = 73 days
And, the number of days required to finish the same work by Larry = 78 days
And, the number of days required to finish the same work by Justin = 83 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 73 days the work is done by Jonathan = 1
∴ The work done by Jonathan in 1 day = 1/73
Similarly,
∵ In 78 days the work is done by Larry = 1
∴ The work done by Larry in 1 day = 1/78
Similarly,
∵ In 83 days the work is done by Justin = 1
∴ The work done by Justin in 1 day = 1/83 part
Now, the work done by Jonathan, Larry, and Justin together in 1 day
= Jonathan's 1 day work + Larry's 1 day work + Justin's 1 day work
= 1/73 + 1/78 + 1/83
= 6474 + 6059 + 5694/472602
= 18227/472602 part of work
This means in 1 day, 18227/472602 part of work is done by Jonathan, Larry and Justin working together.
Now, the number of days required to finish 18227/472602 part of work by Jonathan, Larry, and Justin working together = 1
∴ the number of days required to finish the whole work (1 work) by Jonathan + Larry + Justin together
= 1/18227/472602
= 1 × 472602/18227 = 472602/18227 days
= 25 16927/18227 days = or 25.929 days
Thus, Jonathan, Larry, and Justin working together will finish the total work (1 work) in 25 16927/18227 days = or 25.929 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 Jonathan = 73 days
And the number of days required to finish the same work by Larry = 78 days
And the number of days required to finish the work by Justin = 83 days
Thus, the number of days required to finish the work by Jonathan, Larry, and Justin together = ?
Here a = 73 days
And, b = 78 days
And, c = 83 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jonathan, Larry, and Justin working together
= 73 × 78 × 83/73 × 78 + 73 × 83 + 78 × 83 days
= 472602/5694 + 6059 + 6474 days
= 472602/18227 days
= 472602/18227 days
= 25 16927/18227 days or 25.929
Thus, Jonathan, Larry, and Justin together will finish the work in 25 16927/18227 days or 25.929 days Answer
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