Question:
Mary can finish a work in 6 days. Jennifer can finish the same work in 11 days while Linda can finish the work in 16 days. How long will it take to finish it if they work together?
Correct Answer
3 21/169 days or 3.124 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Mary = 6 days
And, the number of days required to finish the same work by Jennifer = 11 days
And, the number of days required to finish the same work by Linda = 16 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 6 days the work is done by Mary = 1
∴ The work done by Mary in 1 day = 1/6
Similarly,
∵ In 11 days the work is done by Jennifer = 1
∴ The work done by Jennifer in 1 day = 1/11
Similarly,
∵ In 16 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/16 part
Now, the work done by Mary, Jennifer, and Linda together in 1 day
= Mary's 1 day work + Jennifer's 1 day work + Linda's 1 day work
= 1/6 + 1/11 + 1/16
= 88 + 48 + 33/528
= 169/528 part of work
This means in 1 day, 169/528 part of work is done by Mary, Jennifer and Linda working together.
Now, the number of days required to finish 169/528 part of work by Mary, Jennifer, and Linda working together = 1
∴ the number of days required to finish the whole work (1 work) by Mary + Jennifer + Linda together
= 1/169/528
= 1 × 528/169 = 528/169 days
= 3 21/169 days = or 3.124 days
Thus, Mary, Jennifer, and Linda working together will finish the total work (1 work) in 3 21/169 days = or 3.124 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 Mary = 6 days
And the number of days required to finish the same work by Jennifer = 11 days
And the number of days required to finish the work by Linda = 16 days
Thus, the number of days required to finish the work by Mary, Jennifer, and Linda together = ?
Here a = 6 days
And, b = 11 days
And, c = 16 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Mary, Jennifer, and Linda working together
= 6 × 11 × 16/6 × 11 + 6 × 16 + 11 × 16 days
= 1056/66 + 96 + 176 days
= 1056/338 days
= 1056/338 days
= 1056 ÷ 2/338 ÷ 2 = 528/169 days
= 3 21/169 days or 3.124
Thus, Mary, Jennifer, and Linda together will finish the work in 3 21/169 days or 3.124 days Answer
Similar Questions
(1) Kenneth can finish a work in 41 days. Kevin can finish the same work in 42 days while Brian can finish the work in 43 days. How long will it take to finish it if they work together?
(2) If James can finish the work in 2 days and John can finish the same work in 6 days, then in how many days both can finish the work together?
(3) Donna can finish a work in 42 days. Carol can finish the same work in 47 days while Amanda can finish the work in 52 days. How long will it take to finish it if they work together?
(4) If Edward can finish the work in 57 days and Nathan can finish the same work in 62 days, then in how many days both can finish the work together?
(5) If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?
(6) 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?
(7) Ryan can finish a work in 63 days. Gary can finish the same work in 68 days while Nicholas can finish the work in 73 days. How long will it take to finish it if they work together?
(8) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?
(9) Susan can finish a work in 18 days. Sarah can finish the same work in 23 days while Karen can finish the work in 28 days. How long will it take to finish it if they work together?
(10) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?