Question:
Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?
Correct Answer
17 7823/8723 days or 17.897 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Brian = 49 days
And, the number of days required to finish the same work by Timothy = 54 days
And, the number of days required to finish the same work by Ronald = 59 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 49 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/49
Similarly,
∵ In 54 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/54
Similarly,
∵ In 59 days the work is done by Ronald = 1
∴ The work done by Ronald in 1 day = 1/59 part
Now, the work done by Brian, Timothy, and Ronald together in 1 day
= Brian's 1 day work + Timothy's 1 day work + Ronald's 1 day work
= 1/49 + 1/54 + 1/59
= 3186 + 2891 + 2646/156114
= 8723/156114 part of work
This means in 1 day, 8723/156114 part of work is done by Brian, Timothy and Ronald working together.
Now, the number of days required to finish 8723/156114 part of work by Brian, Timothy, and Ronald working together = 1
∴ the number of days required to finish the whole work (1 work) by Brian + Timothy + Ronald together
= 1/8723/156114
= 1 × 156114/8723 = 156114/8723 days
= 17 7823/8723 days = or 17.897 days
Thus, Brian, Timothy, and Ronald working together will finish the total work (1 work) in 17 7823/8723 days = or 17.897 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 Brian = 49 days
And the number of days required to finish the same work by Timothy = 54 days
And the number of days required to finish the work by Ronald = 59 days
Thus, the number of days required to finish the work by Brian, Timothy, and Ronald together = ?
Here a = 49 days
And, b = 54 days
And, c = 59 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Brian, Timothy, and Ronald working together
= 49 × 54 × 59/49 × 54 + 49 × 59 + 54 × 59 days
= 156114/2646 + 2891 + 3186 days
= 156114/8723 days
= 156114/8723 days
= 17 7823/8723 days or 17.897
Thus, Brian, Timothy, and Ronald together will finish the work in 17 7823/8723 days or 17.897 days Answer
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