Question 265453: 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.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 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,
32 0
16 16
then a third of the water in the second jar into the first,
16+16/3 16-16/3
then a fourth of the water in the first jar into the second,
3/4(16+16/3) (16-16/3)+1/4(16+16/3)
then a fifth of the water in the second jar into the first,
3/4(16+16/3)+1/5*(16-16/3)+1/4(16+16/3) 4/5*(16-16/3)+1/4(16+16/3)
352/15 and 208/15
after pour five
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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