Question : Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?
Correct Answer 32 13864/14689 days or 32.944 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Rachel = 94 days
And, the number of days required to finish the same work by Janet = 99 days
And, the number of days required to finish the same work by Catherine = 104 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 94 days the work is done by Rachel = 1
∴ The work done by Rachel in 1 day = 1/94
Similarly,
∵ In 99 days the work is done by Janet = 1
∴ The work done by Janet in 1 day = 1/99
Similarly,
∵ In 104 days the work is done by Catherine = 1
∴ The work done by Catherine in 1 day = 1/104 part
Now, the work done by Rachel, Janet, and Catherine together in 1 day
= Rachel's 1 day work + Janet's 1 day work + Catherine's 1 day work
= 1/94 + 1/99 + 1/104
= 5148 + 4888 + 4653/483912
= 14689/483912 part of work
This means in 1 day, 14689/483912 part of work is done by Rachel, Janet and Catherine working together.
Now, the number of days required to finish 14689/483912 part of work by Rachel, Janet, and Catherine working together = 1
∴ the number of days required to finish the whole work (1 work) by Rachel + Janet + Catherine together
= 1/14689/483912
= 1 × 483912/14689 = 483912/14689 days
= 32 13864/14689 days = or 32.944 days
Thus, Rachel, Janet, and Catherine working together will finish the total work (1 work) in 32 13864/14689 days = or 32.944 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 Rachel = 94 days
And the number of days required to finish the same work by Janet = 99 days
And the number of days required to finish the work by Catherine = 104 days
Thus, the number of days required to finish the work by Rachel, Janet, and Catherine together = ?
Here a = 94 days
And, b = 99 days
And, c = 104 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Rachel, Janet, and Catherine working together
= 94 × 99 × 104/94 × 99 + 94 × 104 + 99 × 104 days
= 967824/9306 + 9776 + 10296 days
= 967824/29378 days
= 967824/29378 days
= 967824 ÷ 2/29378 ÷ 2 = 483912/14689 days
= 32 13864/14689 days or 32.944
Thus, Rachel, Janet, and Catherine together will finish the work in 32 13864/14689 days or 32.944 days Answer
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