Question:
Michael can finish a work in 7 days. David can finish the same work in 8 days while William can finish the work in 9 days. How long will it take to finish it if they work together?
Correct Answer
2 122/191 days or 2.639 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Michael = 7 days
And, the number of days required to finish the same work by David = 8 days
And, the number of days required to finish the same work by William = 9 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 7 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/7
Similarly,
∵ In 8 days the work is done by David = 1
∴ The work done by David in 1 day = 1/8
Similarly,
∵ In 9 days the work is done by William = 1
∴ The work done by William in 1 day = 1/9 part
Now, the work done by Michael, David, and William together in 1 day
= Michael's 1 day work + David's 1 day work + William's 1 day work
= 1/7 + 1/8 + 1/9
= 72 + 63 + 56/504
= 191/504 part of work
This means in 1 day, 191/504 part of work is done by Michael, David and William working together.
Now, the number of days required to finish 191/504 part of work by Michael, David, and William working together = 1
∴ the number of days required to finish the whole work (1 work) by Michael + David + William together
= 1/191/504
= 1 × 504/191 = 504/191 days
= 2 122/191 days = or 2.639 days
Thus, Michael, David, and William working together will finish the total work (1 work) in 2 122/191 days = or 2.639 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 Michael = 7 days
And the number of days required to finish the same work by David = 8 days
And the number of days required to finish the work by William = 9 days
Thus, the number of days required to finish the work by Michael, David, and William together = ?
Here a = 7 days
And, b = 8 days
And, c = 9 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Michael, David, and William working together
= 7 × 8 × 9/7 × 8 + 7 × 9 + 8 × 9 days
= 504/56 + 63 + 72 days
= 504/191 days
= 504/191 days
= 2 122/191 days or 2.639
Thus, Michael, David, and William together will finish the work in 2 122/191 days or 2.639 days Answer
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