Question:
Jack can finish a work in 99 days. Jerry can finish the same work in 104 days while Tyler can finish the work in 109 days. How long will it take to finish it if they work together?
Correct Answer
34 19882/32423 days or 34.613 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jack = 99 days
And, the number of days required to finish the same work by Jerry = 104 days
And, the number of days required to finish the same work by Tyler = 109 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 99 days the work is done by Jack = 1
∴ The work done by Jack in 1 day = 1/99
Similarly,
∵ In 104 days the work is done by Jerry = 1
∴ The work done by Jerry in 1 day = 1/104
Similarly,
∵ In 109 days the work is done by Tyler = 1
∴ The work done by Tyler in 1 day = 1/109 part
Now, the work done by Jack, Jerry, and Tyler together in 1 day
= Jack's 1 day work + Jerry's 1 day work + Tyler's 1 day work
= 1/99 + 1/104 + 1/109
= 11336 + 10791 + 10296/1122264
= 32423/1122264 part of work
This means in 1 day, 32423/1122264 part of work is done by Jack, Jerry and Tyler working together.
Now, the number of days required to finish 32423/1122264 part of work by Jack, Jerry, and Tyler working together = 1
∴ the number of days required to finish the whole work (1 work) by Jack + Jerry + Tyler together
= 1/32423/1122264
= 1 × 1122264/32423 = 1122264/32423 days
= 34 19882/32423 days = or 34.613 days
Thus, Jack, Jerry, and Tyler working together will finish the total work (1 work) in 34 19882/32423 days = or 34.613 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 Jack = 99 days
And the number of days required to finish the same work by Jerry = 104 days
And the number of days required to finish the work by Tyler = 109 days
Thus, the number of days required to finish the work by Jack, Jerry, and Tyler together = ?
Here a = 99 days
And, b = 104 days
And, c = 109 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jack, Jerry, and Tyler working together
= 99 × 104 × 109/99 × 104 + 99 × 109 + 104 × 109 days
= 1122264/10296 + 10791 + 11336 days
= 1122264/32423 days
= 1122264/32423 days
= 34 19882/32423 days or 34.613
Thus, Jack, Jerry, and Tyler together will finish the work in 34 19882/32423 days or 34.613 days Answer
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