Question:
Barbara can finish a work in 12 days. Susan can finish the same work in 13 days while Jessica can finish the work in 14 days. How long will it take to finish it if they work together?
Correct Answer
4 80/253 days or 4.316 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Barbara = 12 days
And, the number of days required to finish the same work by Susan = 13 days
And, the number of days required to finish the same work by Jessica = 14 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 Barbara = 1
∴ The work done by Barbara in 1 day = 1/12
Similarly,
∵ In 13 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/13
Similarly,
∵ In 14 days the work is done by Jessica = 1
∴ The work done by Jessica in 1 day = 1/14 part
Now, the work done by Barbara, Susan, and Jessica together in 1 day
= Barbara's 1 day work + Susan's 1 day work + Jessica's 1 day work
= 1/12 + 1/13 + 1/14
= 91 + 84 + 78/1092
= 253/1092 part of work
This means in 1 day, 253/1092 part of work is done by Barbara, Susan and Jessica working together.
Now, the number of days required to finish 253/1092 part of work by Barbara, Susan, and Jessica working together = 1
∴ the number of days required to finish the whole work (1 work) by Barbara + Susan + Jessica together
= 1/253/1092
= 1 × 1092/253 = 1092/253 days
= 4 80/253 days = or 4.316 days
Thus, Barbara, Susan, and Jessica working together will finish the total work (1 work) in 4 80/253 days = or 4.316 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 Barbara = 12 days
And the number of days required to finish the same work by Susan = 13 days
And the number of days required to finish the work by Jessica = 14 days
Thus, the number of days required to finish the work by Barbara, Susan, and Jessica together = ?
Here a = 12 days
And, b = 13 days
And, c = 14 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Barbara, Susan, and Jessica working together
= 12 × 13 × 14/12 × 13 + 12 × 14 + 13 × 14 days
= 2184/156 + 168 + 182 days
= 2184/506 days
= 2184/506 days
= 2184 ÷ 2/506 ÷ 2 = 1092/253 days
= 4 80/253 days or 4.316
Thus, Barbara, Susan, and Jessica together will finish the work in 4 80/253 days or 4.316 days Answer
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