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Math Help - word problem, please help

  1. #1
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    Smile word problem, please help

    a swiming pool can be filled in 12 hours and emptied in 15 hours. One day while the pool is being filled, the drain is accidentally left open. It is discovered after 3 hours and the drain is closed. How much longer will it take to fill the pool? Write an equation and solve it. ____I have been trying to write the equation, but seem like I am mistaking somewhere. If I have the right equation , I don't have a problem solving it, so Please help me anyone. Thank you!
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  2. #2
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    Since it takes 12 hours to fill the pool, 1/12th of the pool can be filled in one hour. Since it takes 15 hours to drain the pool, 1/15th of the pool is drained in one hour.

    But it drains slightly slower than it can be filled. If the drain was left open, then 3(\frac{1}{12}-\frac{1}{15})=\frac{1}{20}th of the pool was filled in that three hours. Therefore, 19/20 remains to be filled.

    Since the plug is now in place, 12(19/20)=11.4 hours to finish filling the pool.
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  3. #3
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    the way I was trying to solve it was 1/12 -1/15 = 1/x-3 and I was trying to solve for x. I can't find the right way to put the problem in equation. Your answer make sense. Can you help me how to put it in an equation. Thanks!
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  4. #4
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    Here ya' go:

    3(\frac{1}{12}-\frac{1}{15})+\frac{t}{12}=1
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  5. #5
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    reply

    after solving the equation t = 6 The way I used to place it in equation was 3(1/12-1/15)=1/x I solved for x and the answer was x=20. Do you think I was wrong? Should I change it to 3(1/12-1/15)+t/12=1 ?
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  6. #6
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    The way you had it set up originally is the amount of the pool that was filled while the plug was out.

    If you solve the last equation posted, you get t=57/5=11.4. It accounts for the amount of the pool to be filled ater the plug was put back in.
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  7. #7
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    Word Problem

    Your question was "how much longer will it take to fill the pool?".

    That is, had the drain not been open and it took say 10 hours to fill, but with the drain open it took 12 hours, then the answer is 2 hours, not 12 hours. Because "how much LONGER will it take to fill the pool?".

    Let the volume of the pool be V.

    To empty the pool it takes 15 hours. The drain was open for 3 hours. Hence

    (3 hours/15 hours) *V, that is V/5 of water ran off.

    Now we have to fill this volume, ie replace this loss.

    To fill V it takes 12 hours
    To fill (V/5), that is the water that ran off, it takes how much?

    Clearly it takes 1/5 of 12 hours, ie 2.4 hours, ie 2 hours 24 minutes.

    If the preceding line is not clear, then from simple proportion:

    To fill V it takes 12 hours

    To fill (V/5) it takes x.

    Hence, (x ) / (12 hours) = (V/5)/V

    Whence x= (V/5)/(V)*(12 hours) = 2.4 hours.

    0.4 hours = (60 minutes) * (0.4)
    = 24 minutes

    So 2.4 hours = 2hrs 24mins.

    Again, this is not the time needed to fill whole pool but to replace the water that been mistakenly drained off.
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  8. #8
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    pool filling

    size of pool not relevant. pick asize. say 10,000 gals. calculate a fill rate and adrain rate. the difference is the rate of gain of fill over drain since fill is faster than drain. during fill calculate the amount accumulated. subtract this value from 10000 gals.then calculate the fill time. new volume divided by fill rate.
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