SOLUTION: if a pond takes 40 days to be fulfilled if water level twice each day how longittakess to be fulfilled 1/4 of the pond????

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Question 1068452: if a pond takes 40 days to be fulfilled if water level twice each day how longittakess to be fulfilled 1/4 of the pond????
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure I get it, but here goes:
If the water level doubles each day and it takes 40
days to fill the pond, how long does it take to
fill 1/4 of the pond?
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I'll start with the water level at +h%280%29+ units ( any units of length )
I can say:
+h%280%29%2A2%5E40+| is the full level.
Now I want to take +1%2F4+ of that
+%281%2F4%29%2Ah%280%29%2A2%5E40+ is the 1/4 full level
Now let +t+ = the number of days it takes to reach +1%2F4+ fiull
+%281%2F4%29%2Ah%280%29%2A2%5E40+=+h%280%29%2A2%5Et+
+2%5E40+=+4%2A2%5Et+
+2%5E40+=+2%5E2%2A2%5Et+
+2%5E40+=+2%5E%28+t+%2B+2+%29+
+40+=+t+%2B+2+
+t+=+38+
It takes 38 days to be 1/4 filled
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+2%5E40+=+2%5E%28+t%2B2+%29+
Definitely get another opinion on this.
I don't know how to prove this result