Question:
Jason can finish a work in 59 days. Ryan can finish the same work in 64 days while Jacob can finish the work in 69 days. How long will it take to finish it if they work together?
Correct Answer
21 3021/12263 days or 21.246 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jason = 59 days
And, the number of days required to finish the same work by Ryan = 64 days
And, the number of days required to finish the same work by Jacob = 69 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 59 days the work is done by Jason = 1
∴ The work done by Jason in 1 day = 1/59
Similarly,
∵ In 64 days the work is done by Ryan = 1
∴ The work done by Ryan in 1 day = 1/64
Similarly,
∵ In 69 days the work is done by Jacob = 1
∴ The work done by Jacob in 1 day = 1/69 part
Now, the work done by Jason, Ryan, and Jacob together in 1 day
= Jason's 1 day work + Ryan's 1 day work + Jacob's 1 day work
= 1/59 + 1/64 + 1/69
= 4416 + 4071 + 3776/260544
= 12263/260544 part of work
This means in 1 day, 12263/260544 part of work is done by Jason, Ryan and Jacob working together.
Now, the number of days required to finish 12263/260544 part of work by Jason, Ryan, and Jacob working together = 1
∴ the number of days required to finish the whole work (1 work) by Jason + Ryan + Jacob together
= 1/12263/260544
= 1 × 260544/12263 = 260544/12263 days
= 21 3021/12263 days = or 21.246 days
Thus, Jason, Ryan, and Jacob working together will finish the total work (1 work) in 21 3021/12263 days = or 21.246 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 Jason = 59 days
And the number of days required to finish the same work by Ryan = 64 days
And the number of days required to finish the work by Jacob = 69 days
Thus, the number of days required to finish the work by Jason, Ryan, and Jacob together = ?
Here a = 59 days
And, b = 64 days
And, c = 69 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jason, Ryan, and Jacob working together
= 59 × 64 × 69/59 × 64 + 59 × 69 + 64 × 69 days
= 260544/3776 + 4071 + 4416 days
= 260544/12263 days
= 260544/12263 days
= 21 3021/12263 days or 21.246
Thus, Jason, Ryan, and Jacob together will finish the work in 21 3021/12263 days or 21.246 days Answer
Similar Questions
(1) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?
(2) Kimberly can finish a work in 34 days. Emily can finish the same work in 35 days while Donna can finish the work in 36 days. How long will it take to finish it if they work together?
(3) If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?
(4) If Thomas can finish the work in 21 days and Andrew can finish the same work in 26 days, then in how many days both can finish the work together?
(5) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?
(6) 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?
(7) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?
(8) Dorothy can finish a work in 46 days. Melissa can finish the same work in 47 days while Deborah can finish the work in 48 days. How long will it take to finish it if they work together?
(9) Cynthia can finish a work in 64 days. Amy can finish the same work in 69 days while Angela can finish the work in 74 days. How long will it take to finish it if they work together?
(10) If Robert can finish the work in 4 days and David can finish the same work in 7 days, then in how many days both can finish the work together?