SOLUTION: Kindly answer this word problem: Alex can do a piece of work in 20 days; Allen can do it in 24 days. After the two have been working together in 7 days, they are joined by Andy an

Question 402162: Kindly answer this word problem:
Alex can do a piece of work in 20 days; Allen can do it in 24 days. After the two have been working together in 7 days, they are joined by Andy and the three finish the job in 3 more days. How long will it take Andy to do the job alone?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Alex can do a piece of work in 20 days; Allen can do it in 24 days. After the two have been working together in 7 days, they are joined by Andy and the three finish the job in 3 more days. How long will it take Andy to do the job alone?
.
Amount of work done before Andy joins:
7(1/20 + 1/24)
.
Let x = days it takes Andy to do the work by himself
then
7(1/20 + 1/24)+ 3(1/20 + 1/24 + 1/x) = 1
multiplying both sides by (20)(24)x:
7(24x + 20x)+ 3(24x + 20x + (20)(24)) = (20)(24)x
7(44x)+ 3(44x + 480) = 480x
308x+ 132x + 1440 = 480x
440x + 1440 = 480x
1440 = 40x
36 days = x

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