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 & 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
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