Question:
Linda can finish a work in 12 days. Barbara can finish the same work in 17 days while Susan can finish the work in 22 days. How long will it take to finish it if they work together?
Correct Answer
5 139/421 days or 5.33 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Linda = 12 days
And, the number of days required to finish the same work by Barbara = 17 days
And, the number of days required to finish the same work by Susan = 22 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 12 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/12
Similarly,
∵ In 17 days the work is done by Barbara = 1
∴ The work done by Barbara in 1 day = 1/17
Similarly,
∵ In 22 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/22 part
Now, the work done by Linda, Barbara, and Susan together in 1 day
= Linda's 1 day work + Barbara's 1 day work + Susan's 1 day work
= 1/12 + 1/17 + 1/22
= 187 + 132 + 102/2244
= 421/2244 part of work
This means in 1 day, 421/2244 part of work is done by Linda, Barbara and Susan working together.
Now, the number of days required to finish 421/2244 part of work by Linda, Barbara, and Susan working together = 1
∴ the number of days required to finish the whole work (1 work) by Linda + Barbara + Susan together
= 1/421/2244
= 1 × 2244/421 = 2244/421 days
= 5 139/421 days = or 5.33 days
Thus, Linda, Barbara, and Susan working together will finish the total work (1 work) in 5 139/421 days = or 5.33 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 Linda = 12 days
And the number of days required to finish the same work by Barbara = 17 days
And the number of days required to finish the work by Susan = 22 days
Thus, the number of days required to finish the work by Linda, Barbara, and Susan together = ?
Here a = 12 days
And, b = 17 days
And, c = 22 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Linda, Barbara, and Susan working together
= 12 × 17 × 22/12 × 17 + 12 × 22 + 17 × 22 days
= 4488/204 + 264 + 374 days
= 4488/842 days
= 4488/842 days
= 4488 ÷ 2/842 ÷ 2 = 2244/421 days
= 5 139/421 days or 5.33
Thus, Linda, Barbara, and Susan together will finish the work in 5 139/421 days or 5.33 days Answer
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