Question:
Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?
Correct Answer
1 13/47 days or 1.277 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Robert = 3 days
And, the number of days required to finish the same work by John = 4 days
And, the number of days required to finish the same work by Michael = 5 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 3 days the work is done by Robert = 1
∴ The work done by Robert in 1 day = 1/3
Similarly,
∵ In 4 days the work is done by John = 1
∴ The work done by John in 1 day = 1/4
Similarly,
∵ In 5 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/5 part
Now, the work done by Robert, John, and Michael together in 1 day
= Robert's 1 day work + John's 1 day work + Michael's 1 day work
= 1/3 + 1/4 + 1/5
= 20 + 15 + 12/60
= 47/60 part of work
This means in 1 day, 47/60 part of work is done by Robert, John and Michael working together.
Now, the number of days required to finish 47/60 part of work by Robert, John, and Michael working together = 1
∴ the number of days required to finish the whole work (1 work) by Robert + John + Michael together
= 1/47/60
= 1 × 60/47 = 60/47 days
= 1 13/47 days = or 1.277 days
Thus, Robert, John, and Michael working together will finish the total work (1 work) in 1 13/47 days = or 1.277 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 Robert = 3 days
And the number of days required to finish the same work by John = 4 days
And the number of days required to finish the work by Michael = 5 days
Thus, the number of days required to finish the work by Robert, John, and Michael together = ?
Here a = 3 days
And, b = 4 days
And, c = 5 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Robert, John, and Michael working together
= 3 × 4 × 5/3 × 4 + 3 × 5 + 4 × 5 days
= 60/12 + 15 + 20 days
= 60/47 days
= 60/47 days
= 1 13/47 days or 1.277
Thus, Robert, John, and Michael together will finish the work in 1 13/47 days or 1.277 days Answer
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