Question:
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?
Correct Answer
2 118/121 days or 2.975 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Linda = 8 days
And, the number of days required to finish the same work by Elizabeth = 9 days
And, the number of days required to finish the same work by Barbara = 10 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 Linda = 1
∴ The work done by Linda in 1 day = 1/8
Similarly,
∵ In 9 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/9
Similarly,
∵ In 10 days the work is done by Barbara = 1
∴ The work done by Barbara in 1 day = 1/10 part
Now, the work done by Linda, Elizabeth, and Barbara together in 1 day
= Linda's 1 day work + Elizabeth's 1 day work + Barbara's 1 day work
= 1/8 + 1/9 + 1/10
= 45 + 40 + 36/360
= 121/360 part of work
This means in 1 day, 121/360 part of work is done by Linda, Elizabeth and Barbara working together.
Now, the number of days required to finish 121/360 part of work by Linda, Elizabeth, and Barbara working together = 1
∴ the number of days required to finish the whole work (1 work) by Linda + Elizabeth + Barbara together
= 1/121/360
= 1 × 360/121 = 360/121 days
= 2 118/121 days = or 2.975 days
Thus, Linda, Elizabeth, and Barbara working together will finish the total work (1 work) in 2 118/121 days = or 2.975 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 = 8 days
And the number of days required to finish the same work by Elizabeth = 9 days
And the number of days required to finish the work by Barbara = 10 days
Thus, the number of days required to finish the work by Linda, Elizabeth, and Barbara together = ?
Here a = 8 days
And, b = 9 days
And, c = 10 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Linda, Elizabeth, and Barbara working together
= 8 × 9 × 10/8 × 9 + 8 × 10 + 9 × 10 days
= 720/72 + 80 + 90 days
= 720/242 days
= 720/242 days
= 720 ÷ 2/242 ÷ 2 = 360/121 days
= 2 118/121 days or 2.975
Thus, Linda, Elizabeth, and Barbara together will finish the work in 2 118/121 days or 2.975 days Answer
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