Question : Elizabeth can finish a work in 14 days. Susan can finish the same work in 19 days while Jessica can finish the work in 24 days. How long will it take to finish it if they work together?
Correct Answer 6 18/529 days or 6.034 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Elizabeth = 14 days
And, the number of days required to finish the same work by Susan = 19 days
And, the number of days required to finish the same work by Jessica = 24 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 14 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/14
Similarly,
∵ In 19 days the work is done by Susan = 1
∴ The work done by Susan in 1 day = 1/19
Similarly,
∵ In 24 days the work is done by Jessica = 1
∴ The work done by Jessica in 1 day = 1/24 part
Now, the work done by Elizabeth, Susan, and Jessica together in 1 day
= Elizabeth's 1 day work + Susan's 1 day work + Jessica's 1 day work
= 1/14 + 1/19 + 1/24
= 228 + 168 + 133/3192
= 529/3192 part of work
This means in 1 day, 529/3192 part of work is done by Elizabeth, Susan and Jessica working together.
Now, the number of days required to finish 529/3192 part of work by Elizabeth, Susan, and Jessica working together = 1
∴ the number of days required to finish the whole work (1 work) by Elizabeth + Susan + Jessica together
= 1/529/3192
= 1 × 3192/529 = 3192/529 days
= 6 18/529 days = or 6.034 days
Thus, Elizabeth, Susan, and Jessica working together will finish the total work (1 work) in 6 18/529 days = or 6.034 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 Elizabeth = 14 days
And the number of days required to finish the same work by Susan = 19 days
And the number of days required to finish the work by Jessica = 24 days
Thus, the number of days required to finish the work by Elizabeth, Susan, and Jessica together = ?
Here a = 14 days
And, b = 19 days
And, c = 24 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Elizabeth, Susan, and Jessica working together
= 14 × 19 × 24/14 × 19 + 14 × 24 + 19 × 24 days
= 6384/266 + 336 + 456 days
= 6384/1058 days
= 6384/1058 days
= 6384 ÷ 2/1058 ÷ 2 = 3192/529 days
= 6 18/529 days or 6.034
Thus, Elizabeth, Susan, and Jessica together will finish the work in 6 18/529 days or 6.034 days Answer
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