Question:
Kevin can finish a work in 47 days. George can finish the same work in 52 days while Timothy can finish the work in 57 days. How long will it take to finish it if they work together?
Correct Answer
17 1829/8087 days or 17.226 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Kevin = 47 days
And, the number of days required to finish the same work by George = 52 days
And, the number of days required to finish the same work by Timothy = 57 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 Kevin = 1
∴ The work done by Kevin in 1 day = 1/47
Similarly,
∵ In 52 days the work is done by George = 1
∴ The work done by George in 1 day = 1/52
Similarly,
∵ In 57 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/57 part
Now, the work done by Kevin, George, and Timothy together in 1 day
= Kevin's 1 day work + George's 1 day work + Timothy's 1 day work
= 1/47 + 1/52 + 1/57
= 2964 + 2679 + 2444/139308
= 8087/139308 part of work
This means in 1 day, 8087/139308 part of work is done by Kevin, George and Timothy working together.
Now, the number of days required to finish 8087/139308 part of work by Kevin, George, and Timothy working together = 1
∴ the number of days required to finish the whole work (1 work) by Kevin + George + Timothy together
= 1/8087/139308
= 1 × 139308/8087 = 139308/8087 days
= 17 1829/8087 days = or 17.226 days
Thus, Kevin, George, and Timothy working together will finish the total work (1 work) in 17 1829/8087 days = or 17.226 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 Kevin = 47 days
And the number of days required to finish the same work by George = 52 days
And the number of days required to finish the work by Timothy = 57 days
Thus, the number of days required to finish the work by Kevin, George, and Timothy together = ?
Here a = 47 days
And, b = 52 days
And, c = 57 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Kevin, George, and Timothy working together
= 47 × 52 × 57/47 × 52 + 47 × 57 + 52 × 57 days
= 139308/2444 + 2679 + 2964 days
= 139308/8087 days
= 139308/8087 days
= 17 1829/8087 days or 17.226
Thus, Kevin, George, and Timothy together will finish the work in 17 1829/8087 days or 17.226 days Answer
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