Question:
Laura can finish a work in 62 days. Kathleen can finish the same work in 67 days while Amy can finish the work in 72 days. How long will it take to finish it if they work together?
Correct Answer
22 1682/6721 days or 22.25 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Laura = 62 days
And, the number of days required to finish the same work by Kathleen = 67 days
And, the number of days required to finish the same work by Amy = 72 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 62 days the work is done by Laura = 1
∴ The work done by Laura in 1 day = 1/62
Similarly,
∵ In 67 days the work is done by Kathleen = 1
∴ The work done by Kathleen in 1 day = 1/67
Similarly,
∵ In 72 days the work is done by Amy = 1
∴ The work done by Amy in 1 day = 1/72 part
Now, the work done by Laura, Kathleen, and Amy together in 1 day
= Laura's 1 day work + Kathleen's 1 day work + Amy's 1 day work
= 1/62 + 1/67 + 1/72
= 2412 + 2232 + 2077/149544
= 6721/149544 part of work
This means in 1 day, 6721/149544 part of work is done by Laura, Kathleen and Amy working together.
Now, the number of days required to finish 6721/149544 part of work by Laura, Kathleen, and Amy working together = 1
∴ the number of days required to finish the whole work (1 work) by Laura + Kathleen + Amy together
= 1/6721/149544
= 1 × 149544/6721 = 149544/6721 days
= 22 1682/6721 days = or 22.25 days
Thus, Laura, Kathleen, and Amy working together will finish the total work (1 work) in 22 1682/6721 days = or 22.25 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 Laura = 62 days
And the number of days required to finish the same work by Kathleen = 67 days
And the number of days required to finish the work by Amy = 72 days
Thus, the number of days required to finish the work by Laura, Kathleen, and Amy together = ?
Here a = 62 days
And, b = 67 days
And, c = 72 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Laura, Kathleen, and Amy working together
= 62 × 67 × 72/62 × 67 + 62 × 72 + 67 × 72 days
= 299088/4154 + 4464 + 4824 days
= 299088/13442 days
= 299088/13442 days
= 299088 ÷ 2/13442 ÷ 2 = 149544/6721 days
= 22 1682/6721 days or 22.25
Thus, Laura, Kathleen, and Amy together will finish the work in 22 1682/6721 days or 22.25 days Answer
Similar Questions
(1) If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?
(2) Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?
(3) Helen can finish a work in 84 days. Katherine can finish the same work in 89 days while Christine can finish the work in 94 days. How long will it take to finish it if they work together?
(4) Christine can finish a work in 90 days. Rachel can finish the same work in 95 days while Carolyn can finish the work in 100 days. How long will it take to finish it if they work together?
(5) If Paul can finish the work in 39 days and Larry can finish the same work in 44 days, then in how many days both can finish the work together?
(6) If Steven can finish the work in 37 days and Jonathan can finish the same work in 42 days, then in how many days both can finish the work together?
(7) If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?
(8) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?
(9) If Dorothy can finish the work in 47 days and Jack can finish the same work in 51 days, then in how many days both can finish the work together?
(10) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?