Question:
Robert can finish a work in 7 days. Michael can finish the same work in 12 days while David can finish the work in 17 days. How long will it take to finish it if they work together?
Correct Answer
3 207/407 days or 3.509 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Robert = 7 days
And, the number of days required to finish the same work by Michael = 12 days
And, the number of days required to finish the same work by David = 17 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 Robert = 1
∴ The work done by Robert in 1 day = 1/7
Similarly,
∵ In 12 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/12
Similarly,
∵ In 17 days the work is done by David = 1
∴ The work done by David in 1 day = 1/17 part
Now, the work done by Robert, Michael, and David together in 1 day
= Robert's 1 day work + Michael's 1 day work + David's 1 day work
= 1/7 + 1/12 + 1/17
= 204 + 119 + 84/1428
= 407/1428 part of work
This means in 1 day, 407/1428 part of work is done by Robert, Michael and David working together.
Now, the number of days required to finish 407/1428 part of work by Robert, Michael, and David working together = 1
∴ the number of days required to finish the whole work (1 work) by Robert + Michael + David together
= 1/407/1428
= 1 × 1428/407 = 1428/407 days
= 3 207/407 days = or 3.509 days
Thus, Robert, Michael, and David working together will finish the total work (1 work) in 3 207/407 days = or 3.509 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 = 7 days
And the number of days required to finish the same work by Michael = 12 days
And the number of days required to finish the work by David = 17 days
Thus, the number of days required to finish the work by Robert, Michael, and David together = ?
Here a = 7 days
And, b = 12 days
And, c = 17 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Robert, Michael, and David working together
= 7 × 12 × 17/7 × 12 + 7 × 17 + 12 × 17 days
= 1428/84 + 119 + 204 days
= 1428/407 days
= 1428/407 days
= 3 207/407 days or 3.509
Thus, Robert, Michael, and David together will finish the work in 3 207/407 days or 3.509 days Answer
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