Question:
Jason can finish a work in 59 days. Ryan can finish the same work in 64 days while Jacob can finish the work in 69 days. How long will it take to finish it if they work together?
Correct Answer
21 3021/12263 days or 21.246 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jason = 59 days
And, the number of days required to finish the same work by Ryan = 64 days
And, the number of days required to finish the same work by Jacob = 69 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 59 days the work is done by Jason = 1
∴ The work done by Jason in 1 day = 1/59
Similarly,
∵ In 64 days the work is done by Ryan = 1
∴ The work done by Ryan in 1 day = 1/64
Similarly,
∵ In 69 days the work is done by Jacob = 1
∴ The work done by Jacob in 1 day = 1/69 part
Now, the work done by Jason, Ryan, and Jacob together in 1 day
= Jason's 1 day work + Ryan's 1 day work + Jacob's 1 day work
= 1/59 + 1/64 + 1/69
= 4416 + 4071 + 3776/260544
= 12263/260544 part of work
This means in 1 day, 12263/260544 part of work is done by Jason, Ryan and Jacob working together.
Now, the number of days required to finish 12263/260544 part of work by Jason, Ryan, and Jacob working together = 1
∴ the number of days required to finish the whole work (1 work) by Jason + Ryan + Jacob together
= 1/12263/260544
= 1 × 260544/12263 = 260544/12263 days
= 21 3021/12263 days = or 21.246 days
Thus, Jason, Ryan, and Jacob working together will finish the total work (1 work) in 21 3021/12263 days = or 21.246 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 Jason = 59 days
And the number of days required to finish the same work by Ryan = 64 days
And the number of days required to finish the work by Jacob = 69 days
Thus, the number of days required to finish the work by Jason, Ryan, and Jacob together = ?
Here a = 59 days
And, b = 64 days
And, c = 69 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jason, Ryan, and Jacob working together
= 59 × 64 × 69/59 × 64 + 59 × 69 + 64 × 69 days
= 260544/3776 + 4071 + 4416 days
= 260544/12263 days
= 260544/12263 days
= 21 3021/12263 days or 21.246
Thus, Jason, Ryan, and Jacob together will finish the work in 21 3021/12263 days or 21.246 days Answer
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