Question:
Amy can finish a work in 68 days. Shirley can finish the same work in 73 days while Anna can finish the work in 78 days. How long will it take to finish it if they work together?
Correct Answer
24 2052/7981 days or 24.257 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Amy = 68 days
And, the number of days required to finish the same work by Shirley = 73 days
And, the number of days required to finish the same work by Anna = 78 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 68 days the work is done by Amy = 1
∴ The work done by Amy in 1 day = 1/68
Similarly,
∵ In 73 days the work is done by Shirley = 1
∴ The work done by Shirley in 1 day = 1/73
Similarly,
∵ In 78 days the work is done by Anna = 1
∴ The work done by Anna in 1 day = 1/78 part
Now, the work done by Amy, Shirley, and Anna together in 1 day
= Amy's 1 day work + Shirley's 1 day work + Anna's 1 day work
= 1/68 + 1/73 + 1/78
= 2847 + 2652 + 2482/193596
= 7981/193596 part of work
This means in 1 day, 7981/193596 part of work is done by Amy, Shirley and Anna working together.
Now, the number of days required to finish 7981/193596 part of work by Amy, Shirley, and Anna working together = 1
∴ the number of days required to finish the whole work (1 work) by Amy + Shirley + Anna together
= 1/7981/193596
= 1 × 193596/7981 = 193596/7981 days
= 24 2052/7981 days = or 24.257 days
Thus, Amy, Shirley, and Anna working together will finish the total work (1 work) in 24 2052/7981 days = or 24.257 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 Amy = 68 days
And the number of days required to finish the same work by Shirley = 73 days
And the number of days required to finish the work by Anna = 78 days
Thus, the number of days required to finish the work by Amy, Shirley, and Anna together = ?
Here a = 68 days
And, b = 73 days
And, c = 78 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Amy, Shirley, and Anna working together
= 68 × 73 × 78/68 × 73 + 68 × 78 + 73 × 78 days
= 387192/4964 + 5304 + 5694 days
= 387192/15962 days
= 387192/15962 days
= 387192 ÷ 2/15962 ÷ 2 = 193596/7981 days
= 24 2052/7981 days or 24.257
Thus, Amy, Shirley, and Anna together will finish the work in 24 2052/7981 days or 24.257 days Answer
Similar Questions
(1) Justin can finish a work in 79 days. Brandon can finish the same work in 84 days while Benjamin can finish the work in 89 days. How long will it take to finish it if they work together?
(2) Benjamin can finish a work in 85 days. Gregory can finish the same work in 90 days while Alexander can finish the work in 95 days. How long will it take to finish it if they work together?
(3) 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?
(4) Andrew can finish a work in 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?
(5) If Christopher can finish the work in 22 days and Brian can finish the same work in 25 days, then in how many days both can finish the work together?
(6) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?
(7) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 46 days, then in how many days both can finish the work together?
(8) Kimberly can finish a work in 38 days. Donna can finish the same work in 43 days while Michelle can finish the work in 48 days. How long will it take to finish it if they work together?
(9) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?
(10) Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?