SOLUTION: It takes 120 minutes for a hose to fill a swimming pool. If the pool drain is open, it takes 360 minutes to fill the pool. If the pool is full, the hose is off, and drain is open,

Algebra ->  Subset -> SOLUTION: It takes 120 minutes for a hose to fill a swimming pool. If the pool drain is open, it takes 360 minutes to fill the pool. If the pool is full, the hose is off, and drain is open,       Log On


   

Question 981916: It takes 120 minutes for a hose to fill a swimming pool. If the pool drain is open, it takes 360 minutes to fill the pool. If the pool is full, the hose is off, and drain is open, how many minutes does it take to empty the pool?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of filling with just the hose:
[ 1 pool filled ] / [ 120 min ]
Let +r+ = the rate that the
drain by itself empties the pool
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Add the rates of the hose and the drain
open together, but make the drain's rate
negative ( emptying )
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+1%2F120+-+r+=+1%2F360+
+r+=+-+3%2F360+%2B+1%2F360+
+r+=+-1%2F180+ ( it's negative, as it should be )
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So, the drain by itself empties 1 pool in
180 min by itself
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Check:
+1%2F120+-+r+=+1%2F360+
+1%2F120+-+1%2F180+=+1%2F360+
+3%2F360+-+2%2F360+=+1%2F360+
+1%2F360+=+1%2F360+
OK