Question : Sarah can finish a work in 22 days. Lisa can finish the same work in 27 days while Nancy can finish the work in 32 days. How long will it take to finish it if they work together?
Correct Answer 8 856/1081 days or 8.792 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Sarah = 22 days
And, the number of days required to finish the same work by Lisa = 27 days
And, the number of days required to finish the same work by Nancy = 32 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 22 days the work is done by Sarah = 1
∴ The work done by Sarah in 1 day = 1/22
Similarly,
∵ In 27 days the work is done by Lisa = 1
∴ The work done by Lisa in 1 day = 1/27
Similarly,
∵ In 32 days the work is done by Nancy = 1
∴ The work done by Nancy in 1 day = 1/32 part
Now, the work done by Sarah, Lisa, and Nancy together in 1 day
= Sarah's 1 day work + Lisa's 1 day work + Nancy's 1 day work
= 1/22 + 1/27 + 1/32
= 432 + 352 + 297/9504
= 1081/9504 part of work
This means in 1 day, 1081/9504 part of work is done by Sarah, Lisa and Nancy working together.
Now, the number of days required to finish 1081/9504 part of work by Sarah, Lisa, and Nancy working together = 1
∴ the number of days required to finish the whole work (1 work) by Sarah + Lisa + Nancy together
= 1/1081/9504
= 1 × 9504/1081 = 9504/1081 days
= 8 856/1081 days = or 8.792 days
Thus, Sarah, Lisa, and Nancy working together will finish the total work (1 work) in 8 856/1081 days = or 8.792 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 Sarah = 22 days
And the number of days required to finish the same work by Lisa = 27 days
And the number of days required to finish the work by Nancy = 32 days
Thus, the number of days required to finish the work by Sarah, Lisa, and Nancy together = ?
Here a = 22 days
And, b = 27 days
And, c = 32 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Sarah, Lisa, and Nancy working together
= 22 × 27 × 32/22 × 27 + 22 × 32 + 27 × 32 days
= 19008/594 + 704 + 864 days
= 19008/2162 days
= 19008/2162 days
= 19008 ÷ 2/2162 ÷ 2 = 9504/1081 days
= 8 856/1081 days or 8.792
Thus, Sarah, Lisa, and Nancy together will finish the work in 8 856/1081 days or 8.792 days Answer
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