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  1. #1
    Plutonium Lounger
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    Re: Four Hoses, Different Pool

    Don't you require that each hose has been turned on only once, and not turned off before 8 PM? Otherwise, you get a proliferation of solutions (turn on Hose 1 at 1 PM for 10 minutes, then again at 4 PM for 3 minutes etc.)
    And do you require that the times are in whole minutes?

  2. #2
    Plutonium Lounger
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    Re: Four Hoses, Different Pool

    One solution:
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hose 1 fills 8/12 = 40/60 of the pool.
    Hose 2 is turned on at 7:50 PM. It fills 10/60*1/10 = 1/60 of the pool.
    Hose 3 is turned on at 6:48 PM. It fills 72/60*1/8 =9/60 of the pool.
    Hose 4 is turned on at 7:10 PM. It fills 50/60*1/5 = 10/60 of the pool. This hose dispenses 10 times as much as Hose 2.
    Total: 40/60+1/60+9/60+10/60=60/60=1.</span hide>
    There is an infinite number of other solutions.

  3. #3
    Silver Lounger
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    Re: Four Hoses, Different Pool

    <img src=/S/hosed.gif border=0 alt=hosed width=73 height=24> <img src=/S/bwaaah.gif border=0 alt=bwaaah width=123 height=15>

    Odd that the ones I put the most effort into, always have an (almost) infinite number of solutions. I did have one of the 'other' solutions in mind <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

    I had: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hose 1 - 480 minutes, Hose 2 - 64 minutes, Hose 3 - 32 minutes and Hose 4 - 48 minutes. With Hose 1 dispensing 10 X the water as Hose 3.</span hide>
    - Ricky

  4. #4
    Plutonium Lounger
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    Re: Four Hoses, Different Pool

    For example:
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hose 1 runs 480 minutes
    Hose 2 runs 40 minutes
    Hose 3 runs 40 minutes
    Hose 4 runs 55 minutes
    This may be the only one where all running times are multiples of 5 minutes</span hide>
    Or
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hose 1 runs 480 minutes
    Hose 2 runs 50 minutes
    Hose 3 runs 32 minutes
    Hose 4 runs 55 minutes</span hide>
    Or
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Hose 1 runs 480 minutes
    Hose 2 runs 40 minutes
    Hose 3 runs 32 minutes
    Hose 4 runs 60 minutes</span hide>

  5. #5
    Platinum Lounger
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    Re: Four Hoses, Different Pool

    > <font color=red>2. Fractions of a minute are not used. A hose will be switched on when the big hand is on the 12.</font color=red>

    Ah well, if it's all Diophantine Equations that should make it easy! <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

    Alan

  6. #6
    Silver Lounger
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    Four Hoses, Different Pool

    An empty pool needs to be filled. There are four hoses:

    Hose 1 will fill the pool in 12 hours.
    Hose 2 will fill the pool in 10 hours.
    Hose 3 will fill the pool in 8 hours.
    Hose 4 will fill the pool in 5 hours.

    Hose 1 is turned on at 12 noon. The pool becomes exactly filled 8 hours later (at 8:00 p.m.), with all 4 hoses running at that time. Each of the hoses were used for some period of time. One of the hoses dispensed 10 times more water than another of the hoses. What time was hose 2, 3 & 4 switched on? Remember, all four hoses were running at 8:00 p.m. when the pool became filled.

    <font face="Georgia"> <font color=red>As originally posted, the puzzle had too many possible solutions (I thought I was drinking grape juice). Even with the additional conditions given below, there may be multiple solutions. I'll chalk this one up to a poor puzzle and you can chalk it up to a quick math exercise...

    Additional Conditions:
    1. <LI>Hoses can not be switched on and off and on again. Once a hose is switched on, it remains on until 8 PM.
      <LI>Fractions of a minute are not used. A hose will be switched on when the second hand is on the 12.
      <LI>In a fragile attempt to limit the number of correct solutions, each hose must run for a minimum of 32 minutes.
    </font color=red> </font face=georgia>

    <img src=/S/hosed.gif border=0 alt=hosed width=73 height=24>
    - Ricky

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