College Algebra

It takes Todd 3 hours longer than Tom to paint a 4x5 feet bedroom. Working together, both can complete the job in two hours.How long does it take each one to complete the painting job working alone?

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  1. Let it takes Todd X hours; Tom Y hours.
    X=Y+3
    For one hour, Todd paints 1/X part of the bedroom, Tom - 1/Y; together - 1/X+1/Y

    1/(1/X+1/Y)=2
    2(X+Y)=XY
    2(2Y+3)=(Y+3)Y
    4Y+6=Y^2+3Y
    Y^2-Y-6=0 => Y=3, X=6

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