algebra- FINAL UNIT!!

Hi!
My name is Jason,
I needed help studying for tomorrow's test.
The exam is on number problems.
EX. One positive number is 4 times another. IF 240 is divided by each number, the greater quotient exceeds the lesser by 15. Find the two numbers.
Also, there will be some problems on work.
EX. It takes 6 minutes to fill a certain pool and 18 min. to drain the same poll when it is full. With the drain open and the pool empty, how long would it take to fill the pool?
I really need a fast, easy way to solve these types of problems. If you have suggestions, please help out.

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  1. Pick some variables to represent what you are trying to find.
    Here, let:
    X = smaller positive number
    Y = larger positive number
    Algebraically express all the relationships given by the problem.
    Y = 4X

    (240 / X) - 15 = (240 / Y)
    It usually seems to simplify things if you get rid of variables in the denominators of fractions. If both sides of the second equation are multiplied by X * Y it yields:
    240Y - 15XY = 240X.

    Substitute the value for Y from the first equation.
    240(4X) - 15X(4X) = 240X
    960X - 60X^2 = 240X
    divide both sides by 60X
    16 - X = 4
    16 - 4 = X
    X = 12
    Y = 4X
    Y = 48

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  2. ah

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