Question:
Jennifer can finish a work in 10 days. Elizabeth can finish the same work in 15 days while Barbara can finish the work in 20 days. How long will it take to finish it if they work together?
Correct Answer
4 8/13 days or 4.615 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jennifer = 10 days
And, the number of days required to finish the same work by Elizabeth = 15 days
And, the number of days required to finish the same work by Barbara = 20 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 10 days the work is done by Jennifer = 1
∴ The work done by Jennifer in 1 day = 1/10
Similarly,
∵ In 15 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/15
Similarly,
∵ In 20 days the work is done by Barbara = 1
∴ The work done by Barbara in 1 day = 1/20 part
Now, the work done by Jennifer, Elizabeth, and Barbara together in 1 day
= Jennifer's 1 day work + Elizabeth's 1 day work + Barbara's 1 day work
= 1/10 + 1/15 + 1/20
= 6 + 4 + 3/60
= 13/60 part of work
This means in 1 day, 13/60 part of work is done by Jennifer, Elizabeth and Barbara working together.
Now, the number of days required to finish 13/60 part of work by Jennifer, Elizabeth, and Barbara working together = 1
∴ the number of days required to finish the whole work (1 work) by Jennifer + Elizabeth + Barbara together
= 1/13/60
= 1 × 60/13 = 60/13 days
= 4 8/13 days = or 4.615 days
Thus, Jennifer, Elizabeth, and Barbara working together will finish the total work (1 work) in 4 8/13 days = or 4.615 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 Jennifer = 10 days
And the number of days required to finish the same work by Elizabeth = 15 days
And the number of days required to finish the work by Barbara = 20 days
Thus, the number of days required to finish the work by Jennifer, Elizabeth, and Barbara together = ?
Here a = 10 days
And, b = 15 days
And, c = 20 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jennifer, Elizabeth, and Barbara working together
= 10 × 15 × 20/10 × 15 + 10 × 20 + 15 × 20 days
= 3000/150 + 200 + 300 days
= 3000/650 days
= 3000/650 days
= 3000 ÷ 50/650 ÷ 50 = 60/13 days
= 4 8/13 days or 4.615
Thus, Jennifer, Elizabeth, and Barbara together will finish the work in 4 8/13 days or 4.615 days Answer
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