Question:
Stephanie can finish a work in 56 days. Sharon can finish the same work in 61 days while Laura can finish the work in 66 days. How long will it take to finish it if they work together?
Correct Answer
20 1348/5569 days or 20.242 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Stephanie = 56 days
And, the number of days required to finish the same work by Sharon = 61 days
And, the number of days required to finish the same work by Laura = 66 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 56 days the work is done by Stephanie = 1
∴ The work done by Stephanie in 1 day = 1/56
Similarly,
∵ In 61 days the work is done by Sharon = 1
∴ The work done by Sharon in 1 day = 1/61
Similarly,
∵ In 66 days the work is done by Laura = 1
∴ The work done by Laura in 1 day = 1/66 part
Now, the work done by Stephanie, Sharon, and Laura together in 1 day
= Stephanie's 1 day work + Sharon's 1 day work + Laura's 1 day work
= 1/56 + 1/61 + 1/66
= 2013 + 1848 + 1708/112728
= 5569/112728 part of work
This means in 1 day, 5569/112728 part of work is done by Stephanie, Sharon and Laura working together.
Now, the number of days required to finish 5569/112728 part of work by Stephanie, Sharon, and Laura working together = 1
∴ the number of days required to finish the whole work (1 work) by Stephanie + Sharon + Laura together
= 1/5569/112728
= 1 × 112728/5569 = 112728/5569 days
= 20 1348/5569 days = or 20.242 days
Thus, Stephanie, Sharon, and Laura working together will finish the total work (1 work) in 20 1348/5569 days = or 20.242 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 Stephanie = 56 days
And the number of days required to finish the same work by Sharon = 61 days
And the number of days required to finish the work by Laura = 66 days
Thus, the number of days required to finish the work by Stephanie, Sharon, and Laura together = ?
Here a = 56 days
And, b = 61 days
And, c = 66 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Stephanie, Sharon, and Laura working together
= 56 × 61 × 66/56 × 61 + 56 × 66 + 61 × 66 days
= 225456/3416 + 3696 + 4026 days
= 225456/11138 days
= 225456/11138 days
= 225456 ÷ 2/11138 ÷ 2 = 112728/5569 days
= 20 1348/5569 days or 20.242
Thus, Stephanie, Sharon, and Laura together will finish the work in 20 1348/5569 days or 20.242 days Answer
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