Question : Jeffrey can finish a work in 61 days. Jacob can finish the same work in 66 days while Gary can finish the work in 71 days. How long will it take to finish it if they work together?
Correct Answer 21 11943/13043 days or 21.916 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Jeffrey = 61 days
And, the number of days required to finish the same work by Jacob = 66 days
And, the number of days required to finish the same work by Gary = 71 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 61 days the work is done by Jeffrey = 1
∴ The work done by Jeffrey in 1 day = 1/61
Similarly,
∵ In 66 days the work is done by Jacob = 1
∴ The work done by Jacob in 1 day = 1/66
Similarly,
∵ In 71 days the work is done by Gary = 1
∴ The work done by Gary in 1 day = 1/71 part
Now, the work done by Jeffrey, Jacob, and Gary together in 1 day
= Jeffrey's 1 day work + Jacob's 1 day work + Gary's 1 day work
= 1/61 + 1/66 + 1/71
= 4686 + 4331 + 4026/285846
= 13043/285846 part of work
This means in 1 day, 13043/285846 part of work is done by Jeffrey, Jacob and Gary working together.
Now, the number of days required to finish 13043/285846 part of work by Jeffrey, Jacob, and Gary working together = 1
∴ the number of days required to finish the whole work (1 work) by Jeffrey + Jacob + Gary together
= 1/13043/285846
= 1 × 285846/13043 = 285846/13043 days
= 21 11943/13043 days = or 21.916 days
Thus, Jeffrey, Jacob, and Gary working together will finish the total work (1 work) in 21 11943/13043 days = or 21.916 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 Jeffrey = 61 days
And the number of days required to finish the same work by Jacob = 66 days
And the number of days required to finish the work by Gary = 71 days
Thus, the number of days required to finish the work by Jeffrey, Jacob, and Gary together = ?
Here a = 61 days
And, b = 66 days
And, c = 71 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jeffrey, Jacob, and Gary working together
= 61 × 66 × 71/61 × 66 + 61 × 71 + 66 × 71 days
= 285846/4026 + 4331 + 4686 days
= 285846/13043 days
= 285846/13043 days
= 21 11943/13043 days or 21.916
Thus, Jeffrey, Jacob, and Gary together will finish the work in 21 11943/13043 days or 21.916 days Answer
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