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A hose can fill a swimming pool in 4 hours. Another hose needs 9 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?

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  1. Lets think of the situation. It doesn't tell you how big the pool but you can make up a value. To make it easier use a number that it a multiple of both 4 and 9. In this case it would be 36.

    Okay say the pools need 36 gallons of water to be full. To find the rate for each hose divide
    total amount needed/time

    Hose 1: 36/4=9
    Hose 2: 36/9=4

    Hose 1 rate is 9 gallons per hour and Hose 2 rate is 4 gallons per hour

    Add the 2 together 9+4=13 gallons per hour

    Now divide 36 by 13

    36/13= 2.77 Hours

    Is this clear? I know it's long winded but I wanted to explain the full process.

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  2. that helps a lot thank you

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  3. or,

    1/4 + 1/(x+9) = 1/x
    x = 3

    so, the 2nd hose takes 12 hours

    check: in 1 hour, the two hoses fill
    1/4 + 1/12 = 1/3 of the pool.

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