Question : Rebecca can finish a work in 58 days. Laura can finish the same work in 63 days while Cynthia can finish the work in 68 days. How long will it take to finish it if they work together?
Correct Answer 20 5416/5941 days or 20.912 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Rebecca = 58 days
And, the number of days required to finish the same work by Laura = 63 days
And, the number of days required to finish the same work by Cynthia = 68 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 58 days the work is done by Rebecca = 1
∴ The work done by Rebecca in 1 day = 1/58
Similarly,
∵ In 63 days the work is done by Laura = 1
∴ The work done by Laura in 1 day = 1/63
Similarly,
∵ In 68 days the work is done by Cynthia = 1
∴ The work done by Cynthia in 1 day = 1/68 part
Now, the work done by Rebecca, Laura, and Cynthia together in 1 day
= Rebecca's 1 day work + Laura's 1 day work + Cynthia's 1 day work
= 1/58 + 1/63 + 1/68
= 2142 + 1972 + 1827/124236
= 5941/124236 part of work
This means in 1 day, 5941/124236 part of work is done by Rebecca, Laura and Cynthia working together.
Now, the number of days required to finish 5941/124236 part of work by Rebecca, Laura, and Cynthia working together = 1
∴ the number of days required to finish the whole work (1 work) by Rebecca + Laura + Cynthia together
= 1/5941/124236
= 1 × 124236/5941 = 124236/5941 days
= 20 5416/5941 days = or 20.912 days
Thus, Rebecca, Laura, and Cynthia working together will finish the total work (1 work) in 20 5416/5941 days = or 20.912 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 Rebecca = 58 days
And the number of days required to finish the same work by Laura = 63 days
And the number of days required to finish the work by Cynthia = 68 days
Thus, the number of days required to finish the work by Rebecca, Laura, and Cynthia together = ?
Here a = 58 days
And, b = 63 days
And, c = 68 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Rebecca, Laura, and Cynthia working together
= 58 × 63 × 68/58 × 63 + 58 × 68 + 63 × 68 days
= 248472/3654 + 3944 + 4284 days
= 248472/11882 days
= 248472/11882 days
= 248472 ÷ 2/11882 ÷ 2 = 124236/5941 days
= 20 5416/5941 days or 20.912
Thus, Rebecca, Laura, and Cynthia together will finish the work in 20 5416/5941 days or 20.912 days Answer
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