Question:
Edward can finish a work in 57 days. Jeffrey can finish the same work in 62 days while Ryan can finish the work in 67 days. How long will it take to finish it if they work together?
Correct Answer
20 6638/11507 days or 20.577 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Edward = 57 days
And, the number of days required to finish the same work by Jeffrey = 62 days
And, the number of days required to finish the same work by Ryan = 67 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 57 days the work is done by Edward = 1
∴ The work done by Edward in 1 day = 1/57
Similarly,
∵ In 62 days the work is done by Jeffrey = 1
∴ The work done by Jeffrey in 1 day = 1/62
Similarly,
∵ In 67 days the work is done by Ryan = 1
∴ The work done by Ryan in 1 day = 1/67 part
Now, the work done by Edward, Jeffrey, and Ryan together in 1 day
= Edward's 1 day work + Jeffrey's 1 day work + Ryan's 1 day work
= 1/57 + 1/62 + 1/67
= 4154 + 3819 + 3534/236778
= 11507/236778 part of work
This means in 1 day, 11507/236778 part of work is done by Edward, Jeffrey and Ryan working together.
Now, the number of days required to finish 11507/236778 part of work by Edward, Jeffrey, and Ryan working together = 1
∴ the number of days required to finish the whole work (1 work) by Edward + Jeffrey + Ryan together
= 1/11507/236778
= 1 × 236778/11507 = 236778/11507 days
= 20 6638/11507 days = or 20.577 days
Thus, Edward, Jeffrey, and Ryan working together will finish the total work (1 work) in 20 6638/11507 days = or 20.577 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 Edward = 57 days
And the number of days required to finish the same work by Jeffrey = 62 days
And the number of days required to finish the work by Ryan = 67 days
Thus, the number of days required to finish the work by Edward, Jeffrey, and Ryan together = ?
Here a = 57 days
And, b = 62 days
And, c = 67 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Edward, Jeffrey, and Ryan working together
= 57 × 62 × 67/57 × 62 + 57 × 67 + 62 × 67 days
= 236778/3534 + 3819 + 4154 days
= 236778/11507 days
= 236778/11507 days
= 20 6638/11507 days or 20.577
Thus, Edward, Jeffrey, and Ryan together will finish the work in 20 6638/11507 days or 20.577 days Answer
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