Question : Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?
Correct Answer 3 213/241 days or 3.884 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Patricia = 8 days
And, the number of days required to finish the same work by Linda = 13 days
And, the number of days required to finish the same work by Elizabeth = 18 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 8 days the work is done by Patricia = 1
∴ The work done by Patricia in 1 day = 1/8
Similarly,
∵ In 13 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/13
Similarly,
∵ In 18 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/18 part
Now, the work done by Patricia, Linda, and Elizabeth together in 1 day
= Patricia's 1 day work + Linda's 1 day work + Elizabeth's 1 day work
= 1/8 + 1/13 + 1/18
= 117 + 72 + 52/936
= 241/936 part of work
This means in 1 day, 241/936 part of work is done by Patricia, Linda and Elizabeth working together.
Now, the number of days required to finish 241/936 part of work by Patricia, Linda, and Elizabeth working together = 1
∴ the number of days required to finish the whole work (1 work) by Patricia + Linda + Elizabeth together
= 1/241/936
= 1 × 936/241 = 936/241 days
= 3 213/241 days = or 3.884 days
Thus, Patricia, Linda, and Elizabeth working together will finish the total work (1 work) in 3 213/241 days = or 3.884 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 Patricia = 8 days
And the number of days required to finish the same work by Linda = 13 days
And the number of days required to finish the work by Elizabeth = 18 days
Thus, the number of days required to finish the work by Patricia, Linda, and Elizabeth together = ?
Here a = 8 days
And, b = 13 days
And, c = 18 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Patricia, Linda, and Elizabeth working together
= 8 × 13 × 18/8 × 13 + 8 × 18 + 13 × 18 days
= 1872/104 + 144 + 234 days
= 1872/482 days
= 1872/482 days
= 1872 ÷ 2/482 ÷ 2 = 936/241 days
= 3 213/241 days or 3.884
Thus, Patricia, Linda, and Elizabeth together will finish the work in 3 213/241 days or 3.884 days Answer
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