Question:
Scott can finish a work in 81 days. Benjamin can finish the same work in 86 days while Samuel can finish the work in 91 days. How long will it take to finish it if they work together?
Correct Answer
28 13342/22163 days or 28.602 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Scott = 81 days
And, the number of days required to finish the same work by Benjamin = 86 days
And, the number of days required to finish the same work by Samuel = 91 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 81 days the work is done by Scott = 1
∴ The work done by Scott in 1 day = 1/81
Similarly,
∵ In 86 days the work is done by Benjamin = 1
∴ The work done by Benjamin in 1 day = 1/86
Similarly,
∵ In 91 days the work is done by Samuel = 1
∴ The work done by Samuel in 1 day = 1/91 part
Now, the work done by Scott, Benjamin, and Samuel together in 1 day
= Scott's 1 day work + Benjamin's 1 day work + Samuel's 1 day work
= 1/81 + 1/86 + 1/91
= 7826 + 7371 + 6966/633906
= 22163/633906 part of work
This means in 1 day, 22163/633906 part of work is done by Scott, Benjamin and Samuel working together.
Now, the number of days required to finish 22163/633906 part of work by Scott, Benjamin, and Samuel working together = 1
∴ the number of days required to finish the whole work (1 work) by Scott + Benjamin + Samuel together
= 1/22163/633906
= 1 × 633906/22163 = 633906/22163 days
= 28 13342/22163 days = or 28.602 days
Thus, Scott, Benjamin, and Samuel working together will finish the total work (1 work) in 28 13342/22163 days = or 28.602 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 Scott = 81 days
And the number of days required to finish the same work by Benjamin = 86 days
And the number of days required to finish the work by Samuel = 91 days
Thus, the number of days required to finish the work by Scott, Benjamin, and Samuel together = ?
Here a = 81 days
And, b = 86 days
And, c = 91 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Scott, Benjamin, and Samuel working together
= 81 × 86 × 91/81 × 86 + 81 × 91 + 86 × 91 days
= 633906/6966 + 7371 + 7826 days
= 633906/22163 days
= 633906/22163 days
= 28 13342/22163 days or 28.602
Thus, Scott, Benjamin, and Samuel together will finish the work in 28 13342/22163 days or 28.602 days Answer
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