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  1. #1
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    arithmetic problem

    I have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water is in the first jar after the 10th pour? Express your answer as a common fraction.
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  2. #2
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    Hello sri340
    Quote Originally Posted by sri340 View Post
    I have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water is in the first jar after the 10th pour? Express your answer as a common fraction.
    I think it's just \frac{12}{11} pints.

    Set up three columns, showing the number of the pour, and the quantities in each jar after each pour. Like this:
    \begin{array}{c|c|c}<br />
\text{Pour \#} & \text{A} & \text{B}\\<br />
 \hline<br />
0 & 2 & 0\\<br />
1 & 1 & 1\\<br />
2 & \frac43 & \frac23\\<br />
3 & 1 & 1\\<br />
4 & \frac65 & \frac45 \\<br />
5 & 1 & 1\\<br />
... & ... & ...\\<br />
9 & 1 & 1\\<br />
10 & \frac{12}{11} & \frac{10}{11}\\<br />
\end{array}
    After each odd-numbered pour, there's a pint in each jar. So after the 10^{th} pour, where \frac{1}{11} of the quantity in B gets transferred, there'll be \frac{12}{11} pints in A.

    Grandad
    Last edited by Grandad; February 3rd 2010 at 03:17 PM. Reason: Correction to final calculation
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