"An empty pool is filled with water within 5 hours at a decreasing speed. The amount of water filled each hour is a constant part of the amount that was filled the hour before. The amount of water in the first 4 hours is twice the amount in the last 4 hours. In the first 2 hours the amount of water was 48 (cubic meters). Find the pool's volume."
I'm sorry for the poor english, the question is translated... How do I approach this question? I understand this is a geometric sequence but I don't see how it helps me. Any help is appreciated
2026-03-28 04:32:56.1774672376
Geometric Sequence Question - Verbal
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1
Let $V$ be the amount of water poured during the first hour, $kV$ the amount during the second hour, $k^2V$ the amount during the third hour, and so on. Then during the first 4 hours the amount of water is $(1+k+k^2+k^3)V$ and during the last 4 hours it is $(k+k^2+k^3+k^4)V = k(1+k+k^2+k^3)V$. So you get $k=1/2$ and from the condition $(1+k)V=48$ you can compute $V$ too. The rest should be straightforward.