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Math Help - Help with hoses please!

  1. #1
    pochoa
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    Help with hoses please!

    Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 20% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?

    I came up with 9h and 11h. Please help!
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by pochoa
    Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 h using both hoses. They also know that Bob's hose, used alone, takes 20% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?

    I came up with 9h and 11h. Please help!
    Hello,

    I'm very sorry, but your answer couldn't be right because one hose needs a lot more time to fill the swimmingpool than both hoses together.

    Let's have another try:

    (I use SP as abbreviation for "swimmingpool")

    Bob's hose needs b hours to fill the SP.
    Jim's hose needs j hours to fill the SP.
    That means:
    Bob's hose delivers  \frac{SP}{b} per hour.
    Jim's hose delivers  \frac{SP}{j} per hour.
    Both hoses together delivers  \frac{SP}{b}+\frac{SP}{j} per hour.
    They need 18 hours to fill the SP:
     18 \cdot \left( \frac{SP}{b}+\frac{SP}{j} \right)=SP
    Expanded:
      \frac{18 \cdot SP}{b}+\frac{18 \cdot SP}{j} =SP
    Divide both sides of the equation by SP and you get:
      \frac{18}{b}+\frac{18}{j} =1

    As we know that b=0.8 \cdot j we can substitute b by j:
      \frac{18}{0.8 \cdot j}+\frac{18}{j} =1

    I leave the next steps to you.

    As the final result you'll get b=32.4 hrs (32 h; 24 min) and j = 40.5 hrs (40 h; 30 min).

    Bye
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