It is all about work

Algebra Level 2

Sky, Lee and Marvin can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but Marvin left 4 days before the completion of the work. In how many days was the work completed?

13 days 10 days 14 days 11 days 12 days

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2 solutions

Saya Suka
Mar 25, 2021

d/24 + d/30 + (d-4)/40 = d/d = 1

12d - 12 = 120

d = 11 days

Marvin leaving dragged another day until completion.

Roger Erisman
Mar 26, 2021

Let x= days for all three to finish. 1/x = amount done per day.

1/24+1/30+1/40 = 1/x. Multiply by common denominator 120x.

5x + 4x + 3x = 120. Therefore x = 10.

But last four days only Sky and Lee worked.

They did 4/24 + 4/30 = 9/30 of job.

So all three did 21/30 of job. Let y = days to do that.

y/24 + y/30 + y/40 = 21/30. Multiply by CD = 120.

5y + 4y + 3y = 84 so y = 7

7 (all 3 people) + 4(2 people) = 11 days

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