Question:
Ryan can finish a work in 63 days. Gary can finish the same work in 68 days while Nicholas can finish the work in 73 days. How long will it take to finish it if they work together?
Correct Answer
22 8098/13847 days or 22.585 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Ryan = 63 days
And, the number of days required to finish the same work by Gary = 68 days
And, the number of days required to finish the same work by Nicholas = 73 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 63 days the work is done by Ryan = 1
∴ The work done by Ryan in 1 day = 1/63
Similarly,
∵ In 68 days the work is done by Gary = 1
∴ The work done by Gary in 1 day = 1/68
Similarly,
∵ In 73 days the work is done by Nicholas = 1
∴ The work done by Nicholas in 1 day = 1/73 part
Now, the work done by Ryan, Gary, and Nicholas together in 1 day
= Ryan's 1 day work + Gary's 1 day work + Nicholas's 1 day work
= 1/63 + 1/68 + 1/73
= 4964 + 4599 + 4284/312732
= 13847/312732 part of work
This means in 1 day, 13847/312732 part of work is done by Ryan, Gary and Nicholas working together.
Now, the number of days required to finish 13847/312732 part of work by Ryan, Gary, and Nicholas working together = 1
∴ the number of days required to finish the whole work (1 work) by Ryan + Gary + Nicholas together
= 1/13847/312732
= 1 × 312732/13847 = 312732/13847 days
= 22 8098/13847 days = or 22.585 days
Thus, Ryan, Gary, and Nicholas working together will finish the total work (1 work) in 22 8098/13847 days = or 22.585 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 Ryan = 63 days
And the number of days required to finish the same work by Gary = 68 days
And the number of days required to finish the work by Nicholas = 73 days
Thus, the number of days required to finish the work by Ryan, Gary, and Nicholas together = ?
Here a = 63 days
And, b = 68 days
And, c = 73 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Ryan, Gary, and Nicholas working together
= 63 × 68 × 73/63 × 68 + 63 × 73 + 68 × 73 days
= 312732/4284 + 4599 + 4964 days
= 312732/13847 days
= 312732/13847 days
= 22 8098/13847 days or 22.585
Thus, Ryan, Gary, and Nicholas together will finish the work in 22 8098/13847 days or 22.585 days Answer
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