Question:
Donna can finish a work in 42 days. Carol can finish the same work in 47 days while Amanda can finish the work in 52 days. How long will it take to finish it if they work together?
Correct Answer
15 1809/3301 days or 15.548 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Donna = 42 days
And, the number of days required to finish the same work by Carol = 47 days
And, the number of days required to finish the same work by Amanda = 52 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 42 days the work is done by Donna = 1
∴ The work done by Donna in 1 day = 1/42
Similarly,
∵ In 47 days the work is done by Carol = 1
∴ The work done by Carol in 1 day = 1/47
Similarly,
∵ In 52 days the work is done by Amanda = 1
∴ The work done by Amanda in 1 day = 1/52 part
Now, the work done by Donna, Carol, and Amanda together in 1 day
= Donna's 1 day work + Carol's 1 day work + Amanda's 1 day work
= 1/42 + 1/47 + 1/52
= 1222 + 1092 + 987/51324
= 3301/51324 part of work
This means in 1 day, 3301/51324 part of work is done by Donna, Carol and Amanda working together.
Now, the number of days required to finish 3301/51324 part of work by Donna, Carol, and Amanda working together = 1
∴ the number of days required to finish the whole work (1 work) by Donna + Carol + Amanda together
= 1/3301/51324
= 1 × 51324/3301 = 51324/3301 days
= 15 1809/3301 days = or 15.548 days
Thus, Donna, Carol, and Amanda working together will finish the total work (1 work) in 15 1809/3301 days = or 15.548 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 Donna = 42 days
And the number of days required to finish the same work by Carol = 47 days
And the number of days required to finish the work by Amanda = 52 days
Thus, the number of days required to finish the work by Donna, Carol, and Amanda together = ?
Here a = 42 days
And, b = 47 days
And, c = 52 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Donna, Carol, and Amanda working together
= 42 × 47 × 52/42 × 47 + 42 × 52 + 47 × 52 days
= 102648/1974 + 2184 + 2444 days
= 102648/6602 days
= 102648/6602 days
= 102648 ÷ 2/6602 ÷ 2 = 51324/3301 days
= 15 1809/3301 days or 15.548
Thus, Donna, Carol, and Amanda together will finish the work in 15 1809/3301 days or 15.548 days Answer
Similar Questions
(1) Linda can finish a work in 8 days. Elizabeth can finish the same work in 9 days while Barbara can finish the work in 10 days. How long will it take to finish it if they work together?
(2) 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?
(3) If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?
(4) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?
(5) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?
(6) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?
(7) If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?
(8) John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?
(9) If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?
(10) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?