SOLUTION: Since there is a topic for this, it must be a very popular subject. My two questions have to do with painting and pool filling. I haven't had algebra in 38 years and am studying

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Question 139424: Since there is a topic for this, it must be a very popular subject. My two questions have to do with painting and pool filling. I haven't had algebra in 38 years and am studying for an Asset placement test. Can figure most things out except these two.
Susan can paint a house in 4 hours. John can paint a house in 6 hours. If they work together, how long will it take them to paint the house. The answer is 2 hours 24 minutes, but I need to know how to get to that answer.
Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together? Same process here, but can't remember the equation(s).
Any assistance you can give me is appreciated. I have a BS in computer science from 25 years ago, but I still have to take the math placement test to get retraining after losing my job.
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
a task ( painting, pool filling, etc.) that is completed by multiple "inputs" (people, pipes, etc.)
__ is a whole made up of fractions __ the fractions sum to 1 (the whole)

an input's fraction is found by dividing the combined time by the individual time
__ e.g. if A can do a job in 5 hrs, but only takes 3 hours when working with B;
__ A does 3/5 of the job and B does the other 2/5
__ B does 2/5 in 3 hrs, so it would take him 3/(2/5) or 15/2 hr alone

painting: let x="time together" __ (x/4)+(x/6)=1
__ multiplying by 12 __ 3x+2x=12 __ 5x=12 __ x=12/5=2.4=2hr 24min

filling: letx="time together" __ (x/30)+(x/45)+(x/90)=1
__ multiplying by 90 __ 3x+2x+x=90 __ 6x=90 __ x=15

good luck with retraining