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
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