Question:
George can finish a work in 47 days. Timothy can finish the same work in 48 days while Ronald can finish the work in 49 days. How long will it take to finish it if they work together?
Correct Answer
15 6879/6911 days or 15.995 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by George = 47 days
And, the number of days required to finish the same work by Timothy = 48 days
And, the number of days required to finish the same work by Ronald = 49 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 47 days the work is done by George = 1
∴ The work done by George in 1 day = 1/47
Similarly,
∵ In 48 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/48
Similarly,
∵ In 49 days the work is done by Ronald = 1
∴ The work done by Ronald in 1 day = 1/49 part
Now, the work done by George, Timothy, and Ronald together in 1 day
= George's 1 day work + Timothy's 1 day work + Ronald's 1 day work
= 1/47 + 1/48 + 1/49
= 2352 + 2303 + 2256/110544
= 6911/110544 part of work
This means in 1 day, 6911/110544 part of work is done by George, Timothy and Ronald working together.
Now, the number of days required to finish 6911/110544 part of work by George, Timothy, and Ronald working together = 1
∴ the number of days required to finish the whole work (1 work) by George + Timothy + Ronald together
= 1/6911/110544
= 1 × 110544/6911 = 110544/6911 days
= 15 6879/6911 days = or 15.995 days
Thus, George, Timothy, and Ronald working together will finish the total work (1 work) in 15 6879/6911 days = or 15.995 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 George = 47 days
And the number of days required to finish the same work by Timothy = 48 days
And the number of days required to finish the work by Ronald = 49 days
Thus, the number of days required to finish the work by George, Timothy, and Ronald together = ?
Here a = 47 days
And, b = 48 days
And, c = 49 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when George, Timothy, and Ronald working together
= 47 × 48 × 49/47 × 48 + 47 × 49 + 48 × 49 days
= 110544/2256 + 2303 + 2352 days
= 110544/6911 days
= 110544/6911 days
= 15 6879/6911 days or 15.995
Thus, George, Timothy, and Ronald together will finish the work in 15 6879/6911 days or 15.995 days Answer
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