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Math Help - Algebra help

  1. #1
    Dec 2008

    Algebra help

    I suck at word problems. Anyhow, can anyone help me solve/ set this problem up???

    #) An oil tank at Chemco Refinery has two inlet pipes and one outlet pipe. One inlet pipe can fill the tank in 6 hours, and the other inlet pipe can fill the tank in 12 hours. The outlet pipe can EMPTY the tank in 24 hours. How long would it take to fill the tank with all three pipes open?

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  2. #2
    MHF Contributor
    Grandad's Avatar
    Dec 2008
    South Coast of England

    Rate of working

    Hi -

    The usual way of solving problems like this is to find what fraction of the job will be done in a certain time by each of the 'things' that are working (in this case, the 'things' are pipes: 3 of them).

    For instance, the first pipe will fill the tank in 6 hours, so in one hour it will fill one-sixth of the tank.

    Then you do the same for the other 'things'. Then you have to add and subtract fractions, to get an overall picture of what will happen in this amount of time. And finally, work out how much time the whole job will take to complete.

    But if you hate fractions, you can often get around them like this:

    Look at the numbers involved and find their Least Common Multiple. (Don't stop reading - this is simply the smallest number that they'll all divide into without fractions or remainders.)

    Here, the numbers are 6, 12 and 24. So the LCM here is dead easy: it's 24.

    Now a little cheat: just suppose that the tank holds 24 gallons (or litres, or cubic metres, or anything you like, really!). The first pipe takes 6 hours to fill the tank, so it must be pumping in 4 gallons an hour, right?

    Question 1: How many gallons an hour is the second pipe pumping in?

    Question 2: How many gallons are leaking out per hour through the third pipe?

    Question 3: What is the total number of gallons per hour going in to the tank, taking all three pipes into account?

    Question 4: Well then, if the tank holds 24 gallons, how long will it take to fill? (This will involve a fraction, I'm afraid!)

    Notice that it doesn't really matter how much the tank actually holds - the time taken will be the same.

    Hope you can do it now.
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