Question:
Patricia can finish a work in 4 days. Jennifer can finish the same work in 5 days while Linda can finish the work in 6 days. How long will it take to finish it if they work together?
Correct Answer
1 23/37 days or 1.622 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Patricia = 4 days
And, the number of days required to finish the same work by Jennifer = 5 days
And, the number of days required to finish the same work by Linda = 6 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 4 days the work is done by Patricia = 1
∴ The work done by Patricia in 1 day = 1/4
Similarly,
∵ In 5 days the work is done by Jennifer = 1
∴ The work done by Jennifer in 1 day = 1/5
Similarly,
∵ In 6 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/6 part
Now, the work done by Patricia, Jennifer, and Linda together in 1 day
= Patricia's 1 day work + Jennifer's 1 day work + Linda's 1 day work
= 1/4 + 1/5 + 1/6
= 15 + 12 + 10/60
= 37/60 part of work
This means in 1 day, 37/60 part of work is done by Patricia, Jennifer and Linda working together.
Now, the number of days required to finish 37/60 part of work by Patricia, Jennifer, and Linda working together = 1
∴ the number of days required to finish the whole work (1 work) by Patricia + Jennifer + Linda together
= 1/37/60
= 1 × 60/37 = 60/37 days
= 1 23/37 days = or 1.622 days
Thus, Patricia, Jennifer, and Linda working together will finish the total work (1 work) in 1 23/37 days = or 1.622 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 = 4 days
And the number of days required to finish the same work by Jennifer = 5 days
And the number of days required to finish the work by Linda = 6 days
Thus, the number of days required to finish the work by Patricia, Jennifer, and Linda together = ?
Here a = 4 days
And, b = 5 days
And, c = 6 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Patricia, Jennifer, and Linda working together
= 4 × 5 × 6/4 × 5 + 4 × 6 + 5 × 6 days
= 120/20 + 24 + 30 days
= 120/74 days
= 120/74 days
= 120 ÷ 2/74 ÷ 2 = 60/37 days
= 1 23/37 days or 1.622
Thus, Patricia, Jennifer, and Linda together will finish the work in 1 23/37 days or 1.622 days Answer
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