Question:
Brian can finish a work in 45 days. George can finish the same work in 46 days while Timothy can finish the work in 47 days. How long will it take to finish it if they work together?
Correct Answer
15 2085/6347 days or 15.329 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Brian = 45 days
And, the number of days required to finish the same work by George = 46 days
And, the number of days required to finish the same work by Timothy = 47 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 45 days the work is done by Brian = 1
∴ The work done by Brian in 1 day = 1/45
Similarly,
∵ In 46 days the work is done by George = 1
∴ The work done by George in 1 day = 1/46
Similarly,
∵ In 47 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/47 part
Now, the work done by Brian, George, and Timothy together in 1 day
= Brian's 1 day work + George's 1 day work + Timothy's 1 day work
= 1/45 + 1/46 + 1/47
= 2162 + 2115 + 2070/97290
= 6347/97290 part of work
This means in 1 day, 6347/97290 part of work is done by Brian, George and Timothy working together.
Now, the number of days required to finish 6347/97290 part of work by Brian, George, and Timothy working together = 1
∴ the number of days required to finish the whole work (1 work) by Brian + George + Timothy together
= 1/6347/97290
= 1 × 97290/6347 = 97290/6347 days
= 15 2085/6347 days = or 15.329 days
Thus, Brian, George, and Timothy working together will finish the total work (1 work) in 15 2085/6347 days = or 15.329 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 = 45 days
And the number of days required to finish the same work by George = 46 days
And the number of days required to finish the work by Timothy = 47 days
Thus, the number of days required to finish the work by Brian, George, and Timothy together = ?
Here a = 45 days
And, b = 46 days
And, c = 47 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Brian, George, and Timothy working together
= 45 × 46 × 47/45 × 46 + 45 × 47 + 46 × 47 days
= 97290/2070 + 2115 + 2162 days
= 97290/6347 days
= 97290/6347 days
= 15 2085/6347 days or 15.329
Thus, Brian, George, and Timothy together will finish the work in 15 2085/6347 days or 15.329 days Answer
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