Question : Gary can finish a work in 67 days. Eric can finish the same work in 72 days while Jonathan can finish the work in 77 days. How long will it take to finish it if they work together?
Correct Answer 23 14327/15527 days or 23.923 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Gary = 67 days
And, the number of days required to finish the same work by Eric = 72 days
And, the number of days required to finish the same work by Jonathan = 77 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 67 days the work is done by Gary = 1
∴ The work done by Gary in 1 day = 1/67
Similarly,
∵ In 72 days the work is done by Eric = 1
∴ The work done by Eric in 1 day = 1/72
Similarly,
∵ In 77 days the work is done by Jonathan = 1
∴ The work done by Jonathan in 1 day = 1/77 part
Now, the work done by Gary, Eric, and Jonathan together in 1 day
= Gary's 1 day work + Eric's 1 day work + Jonathan's 1 day work
= 1/67 + 1/72 + 1/77
= 5544 + 5159 + 4824/371448
= 15527/371448 part of work
This means in 1 day, 15527/371448 part of work is done by Gary, Eric and Jonathan working together.
Now, the number of days required to finish 15527/371448 part of work by Gary, Eric, and Jonathan working together = 1
∴ the number of days required to finish the whole work (1 work) by Gary + Eric + Jonathan together
= 1/15527/371448
= 1 × 371448/15527 = 371448/15527 days
= 23 14327/15527 days = or 23.923 days
Thus, Gary, Eric, and Jonathan working together will finish the total work (1 work) in 23 14327/15527 days = or 23.923 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 Gary = 67 days
And the number of days required to finish the same work by Eric = 72 days
And the number of days required to finish the work by Jonathan = 77 days
Thus, the number of days required to finish the work by Gary, Eric, and Jonathan together = ?
Here a = 67 days
And, b = 72 days
And, c = 77 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Gary, Eric, and Jonathan working together
= 67 × 72 × 77/67 × 72 + 67 × 77 + 72 × 77 days
= 371448/4824 + 5159 + 5544 days
= 371448/15527 days
= 371448/15527 days
= 23 14327/15527 days or 23.923
Thus, Gary, Eric, and Jonathan together will finish the work in 23 14327/15527 days or 23.923 days Answer
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