Question:
Timothy can finish a work in 49 days. Ronald can finish the same work in 50 days while Edward can finish the work in 51 days. How long will it take to finish it if they work together?
Correct Answer
16 4966/7499 days or 16.662 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Timothy = 49 days
And, the number of days required to finish the same work by Ronald = 50 days
And, the number of days required to finish the same work by Edward = 51 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 49 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/49
Similarly,
∵ In 50 days the work is done by Ronald = 1
∴ The work done by Ronald in 1 day = 1/50
Similarly,
∵ In 51 days the work is done by Edward = 1
∴ The work done by Edward in 1 day = 1/51 part
Now, the work done by Timothy, Ronald, and Edward together in 1 day
= Timothy's 1 day work + Ronald's 1 day work + Edward's 1 day work
= 1/49 + 1/50 + 1/51
= 2550 + 2499 + 2450/124950
= 7499/124950 part of work
This means in 1 day, 7499/124950 part of work is done by Timothy, Ronald and Edward working together.
Now, the number of days required to finish 7499/124950 part of work by Timothy, Ronald, and Edward working together = 1
∴ the number of days required to finish the whole work (1 work) by Timothy + Ronald + Edward together
= 1/7499/124950
= 1 × 124950/7499 = 124950/7499 days
= 16 4966/7499 days = or 16.662 days
Thus, Timothy, Ronald, and Edward working together will finish the total work (1 work) in 16 4966/7499 days = or 16.662 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 Timothy = 49 days
And the number of days required to finish the same work by Ronald = 50 days
And the number of days required to finish the work by Edward = 51 days
Thus, the number of days required to finish the work by Timothy, Ronald, and Edward together = ?
Here a = 49 days
And, b = 50 days
And, c = 51 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Timothy, Ronald, and Edward working together
= 49 × 50 × 51/49 × 50 + 49 × 51 + 50 × 51 days
= 124950/2450 + 2499 + 2550 days
= 124950/7499 days
= 124950/7499 days
= 16 4966/7499 days or 16.662
Thus, Timothy, Ronald, and Edward together will finish the work in 16 4966/7499 days or 16.662 days Answer
Similar Questions
(1) Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?
(2) If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?
(3) If Sarah can finish the work in 19 days and Joshua can finish the same work in 22 days, then in how many days both can finish the work together?
(4) Kenneth can finish a work in 45 days. Brian can finish the same work in 50 days while George can finish the work in 55 days. How long will it take to finish it if they work together?
(5) Donald can finish a work in 35 days. Paul can finish the same work in 40 days while Andrew can finish the work in 45 days. How long will it take to finish it if they work together?
(6) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?
(7) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?
(8) If Thomas can finish the work in 18 days and Andrew can finish the same work in 22 days, then in how many days both can finish the work together?
(9) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?
(10) If Janet can finish the work in 98 days and Russell can finish the same work in 103 days, then in how many days both can finish the work together?