Question:
Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?
Correct Answer
19 391/431 days or 19.907 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Ronald = 55 days
And, the number of days required to finish the same work by Jason = 60 days
And, the number of days required to finish the same work by Jeffrey = 65 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 55 days the work is done by Ronald = 1
∴ The work done by Ronald in 1 day = 1/55
Similarly,
∵ In 60 days the work is done by Jason = 1
∴ The work done by Jason in 1 day = 1/60
Similarly,
∵ In 65 days the work is done by Jeffrey = 1
∴ The work done by Jeffrey in 1 day = 1/65 part
Now, the work done by Ronald, Jason, and Jeffrey together in 1 day
= Ronald's 1 day work + Jason's 1 day work + Jeffrey's 1 day work
= 1/55 + 1/60 + 1/65
= 156 + 143 + 132/8580
= 431/8580 part of work
This means in 1 day, 431/8580 part of work is done by Ronald, Jason and Jeffrey working together.
Now, the number of days required to finish 431/8580 part of work by Ronald, Jason, and Jeffrey working together = 1
∴ the number of days required to finish the whole work (1 work) by Ronald + Jason + Jeffrey together
= 1/431/8580
= 1 × 8580/431 = 8580/431 days
= 19 391/431 days = or 19.907 days
Thus, Ronald, Jason, and Jeffrey working together will finish the total work (1 work) in 19 391/431 days = or 19.907 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 Ronald = 55 days
And the number of days required to finish the same work by Jason = 60 days
And the number of days required to finish the work by Jeffrey = 65 days
Thus, the number of days required to finish the work by Ronald, Jason, and Jeffrey together = ?
Here a = 55 days
And, b = 60 days
And, c = 65 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Ronald, Jason, and Jeffrey working together
= 55 × 60 × 65/55 × 60 + 55 × 65 + 60 × 65 days
= 214500/3300 + 3575 + 3900 days
= 214500/10775 days
= 214500/10775 days
= 214500 ÷ 25/10775 ÷ 25 = 8580/431 days
= 19 391/431 days or 19.907
Thus, Ronald, Jason, and Jeffrey together will finish the work in 19 391/431 days or 19.907 days Answer
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