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Math Help - 2 Word problem I need to turn into an equation and solve.

  1. #1
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    2 Word problem I need to turn into an equation and solve.

    Ok here is Q#1
    A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

    Answer in time?

    Q#2

    Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
    Answer in time?

    PLEASE explain how you got to your answer along with the equation to get to it.

    THANKS FOR YOUR HELP.
    I have no clue on solving this, I am thinking you add up the 2 times together and divide by 2?
    But the water one above I have no clue at all.

    Jo
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  2. #2
    MHF Contributor

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    Quote Originally Posted by bradycat View Post
    Ok here is Q#1
    A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

    Answer in time?
    When two people or things "work together" it is their rates that add. "A tank can be filled by one of two pipes in 12.00 h " means that the filling rate for that pipe is 1 tank/12 h= 1/12 "tanks per hour". "by the other of the two in 1.00 h." means that its filling rate is 1 tank/1 hour= 1 "tanks per hour". Be careful about that third pipe- it is draining, not filling, the tank. That simply means we can treat it "filling" rate as negative. Since it empties the tank in 10.4 hours, its "filling" rate is -1/10.4 "tanks per hour". With all three pipes open their filling rate is 1/12+ 1- 1/10.4 "tanks per hour". You can either convert to decimals by dividing or treat that "1/10.4" as "10/104". Once you have the filling rate of all three in "tanks per hour", the time to fill one tank, "hours per tank" is just the reciprocal.

    Q#2

    Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
    Answer in time?
    Same idea. Bill does the job in 3.8 h so his working rate is 1/3.8 "jobs per hour". John does the job in 5.4 h so his working rate is 1/5.4 "jobs per hour". Working together, their rate is 1/3.8+ 1/5.4. Once you have added those and have their working rate together in "jobs per hour", the time to do one job, "hours per job" is the reciprocal.

    PLEASE explain how you got to your answer along with the equation to get to it.

    THANKS FOR YOUR HELP.
    I have no clue on solving this, I am thinking you add up the 2 times together and divide by 2?
    But the water one above I have no clue at all.

    Jo
    No, you do NOT average the times!
    (Added: well, not the arithetic average. You ARE doing what is called the "harmonic average". The harmonic average of the two numbers a and b is \frac{2}{\frac{1}{a}+ \frac{1}{b}}. You find the arithmetic average of 1/a and 1/b and and invert that.)
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  3. #3
    RRH
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    Quote Originally Posted by bradycat View Post
    Ok here is Q#1
    A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

    Answer in time?

    Q#2

    Bill can do a jobin 3.8 j, and john can do the same job in 5.4h. How will it take them to do the job together? ROUND your answer to the nearest quarter of an hour??
    Answer in time?

    PLEASE explain how you got to your answer along with the equation to get to it.

    THANKS FOR YOUR HELP.
    I have no clue on solving this, I am thinking you add up the 2 times together and divide by 2?
    But the water one above I have no clue at all.

    Jo
    1)Given the information you have provided. Pipe 1 will take 12 hours to fill up 1 tank; therefore, it fills the tank \frac{1}{12} per hour.

    Pipe two can fill 1 tank in 1 hour; therefore, it will fill the tank \frac{1}{1} per hour.

    Drain 1 will take 10.5 hours to drain 1 tank; therefore, it will drain \frac{1}{10.5} per hour.

    Now we apply this information to determine time. The formula should look like this

    (\frac{1}{12}+\frac{1}{1}-\frac{1}{10.5})t=1
    Last edited by RRH; November 21st 2009 at 07:03 AM.
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  4. #4
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    Hi I am still abit lost.
    How do you substract 1/10.5 from 1/12+1/2=
    I can't figure it out.
    Thanks
    j
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  5. #5
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    Talking

    I have tried and I don't know how to add decimal fractions.

    1/3.8 + 1/5.4 = 1
    For the one question about. How to find the LCM for them, is that what you need to do.

    As well as the pipe question.
    NEED HELP PLEASE, and thanks.
    Jo
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