Question : Timothy can finish a work in 53 days. Edward can finish the same work in 58 days while Jason can finish the work in 63 days. How long will it take to finish it if they work together?
Correct Answer 19 2389/10067 days or 19.237 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Timothy = 53 days
And, the number of days required to finish the same work by Edward = 58 days
And, the number of days required to finish the same work by Jason = 63 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 53 days the work is done by Timothy = 1
∴ The work done by Timothy in 1 day = 1/53
Similarly,
∵ In 58 days the work is done by Edward = 1
∴ The work done by Edward in 1 day = 1/58
Similarly,
∵ In 63 days the work is done by Jason = 1
∴ The work done by Jason in 1 day = 1/63 part
Now, the work done by Timothy, Edward, and Jason together in 1 day
= Timothy's 1 day work + Edward's 1 day work + Jason's 1 day work
= 1/53 + 1/58 + 1/63
= 3654 + 3339 + 3074/193662
= 10067/193662 part of work
This means in 1 day, 10067/193662 part of work is done by Timothy, Edward and Jason working together.
Now, the number of days required to finish 10067/193662 part of work by Timothy, Edward, and Jason working together = 1
∴ the number of days required to finish the whole work (1 work) by Timothy + Edward + Jason together
= 1/10067/193662
= 1 × 193662/10067 = 193662/10067 days
= 19 2389/10067 days = or 19.237 days
Thus, Timothy, Edward, and Jason working together will finish the total work (1 work) in 19 2389/10067 days = or 19.237 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 = 53 days
And the number of days required to finish the same work by Edward = 58 days
And the number of days required to finish the work by Jason = 63 days
Thus, the number of days required to finish the work by Timothy, Edward, and Jason together = ?
Here a = 53 days
And, b = 58 days
And, c = 63 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Timothy, Edward, and Jason working together
= 53 × 58 × 63/53 × 58 + 53 × 63 + 58 × 63 days
= 193662/3074 + 3339 + 3654 days
= 193662/10067 days
= 193662/10067 days
= 19 2389/10067 days or 19.237
Thus, Timothy, Edward, and Jason together will finish the work in 19 2389/10067 days or 19.237 days Answer
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