Question:
Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?
Correct Answer
24 9702/16403 days or 24.591 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Nicholas = 69 days
And, the number of days required to finish the same work by Jonathan = 74 days
And, the number of days required to finish the same work by Stephen = 79 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 69 days the work is done by Nicholas = 1
∴ The work done by Nicholas in 1 day = 1/69
Similarly,
∵ In 74 days the work is done by Jonathan = 1
∴ The work done by Jonathan in 1 day = 1/74
Similarly,
∵ In 79 days the work is done by Stephen = 1
∴ The work done by Stephen in 1 day = 1/79 part
Now, the work done by Nicholas, Jonathan, and Stephen together in 1 day
= Nicholas's 1 day work + Jonathan's 1 day work + Stephen's 1 day work
= 1/69 + 1/74 + 1/79
= 5846 + 5451 + 5106/403374
= 16403/403374 part of work
This means in 1 day, 16403/403374 part of work is done by Nicholas, Jonathan and Stephen working together.
Now, the number of days required to finish 16403/403374 part of work by Nicholas, Jonathan, and Stephen working together = 1
∴ the number of days required to finish the whole work (1 work) by Nicholas + Jonathan + Stephen together
= 1/16403/403374
= 1 × 403374/16403 = 403374/16403 days
= 24 9702/16403 days = or 24.591 days
Thus, Nicholas, Jonathan, and Stephen working together will finish the total work (1 work) in 24 9702/16403 days = or 24.591 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 Nicholas = 69 days
And the number of days required to finish the same work by Jonathan = 74 days
And the number of days required to finish the work by Stephen = 79 days
Thus, the number of days required to finish the work by Nicholas, Jonathan, and Stephen together = ?
Here a = 69 days
And, b = 74 days
And, c = 79 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Nicholas, Jonathan, and Stephen working together
= 69 × 74 × 79/69 × 74 + 69 × 79 + 74 × 79 days
= 403374/5106 + 5451 + 5846 days
= 403374/16403 days
= 403374/16403 days
= 24 9702/16403 days or 24.591
Thus, Nicholas, Jonathan, and Stephen together will finish the work in 24 9702/16403 days or 24.591 days Answer
Similar Questions
(1) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?
(2) If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?
(3) Charles can finish a work in 23 days. Daniel can finish the same work in 28 days while Matthew can finish the work in 33 days. How long will it take to finish it if they work together?
(4) Anna can finish a work in 74 days. Pamela can finish the same work in 79 days while Emma can finish the work in 84 days. How long will it take to finish it if they work together?
(5) Helen can finish a work in 84 days. Katherine can finish the same work in 89 days while Christine can finish the work in 94 days. How long will it take to finish it if they work together?
(6) 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?
(7) If Andrew can finish the work in 38 days and Scott can finish the same work in 41 days, then in how many days both can finish the work together?
(8) If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?
(9) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?
(10) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?