SOLUTION: A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 6 hours. The inlet pipe alone can complete the job in one hour l

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Question 1155729: A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 6 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of filling together: +1%2F6+
Rate for the hose alone: +1%2Ft+
Rate for the pipe alone: +1%2F%28+t+-+1+%29+
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+1%2Ft+%2B+1%2F%28+t-1+%29+=+1%2F6+
Multiply both sides by +t%2A%28+t-1+%29%2A6+
+6%2A%28+t-1+%29+%2B+6t+=+t%2A%28+t-1+%29+
+6t+-+6+%2B+6t+=+t%5E2+-+t+
+t%5E2+-+13t+%2B+6+=+0+
I can complete the square:
+t%5E2+-+13t+%2B+%28+-13%2F2+%29%5E2+=+-6+%2B+%28+-13%2F2+%29%5E2+
+t%5E2+-+13t+%2B+169%2F4+=+-24%2F4+%2B+169%2F4+
+t%5E2+-+13t+%2B+169%2F4+=+145%2F4+
+%28+t+-+13%2F2+%29%5E2+=+145%2F4+
+t+-+13%2F2+=+sqrt%28+145+%29+%2F+2+
+t+=+%28+sqrt%28+145+%29+%2B+13+%29+%2F+2+
+t+=+%28+12.0416+%2B+13+%29+%2F+2+
+t+=+25.0416+%2F+2+
+t+=+12.5208+
and
+t+-+1+=+11.5208+
------------------------------
With hose:
12.52 hrs
With pipe:
11.52 hrs
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check:
+1%2Ft+%2B+1%2F%28+t-1+%29+=+1%2F6+
+1%2F12.52+%2B+1%2F11.52+=+1%2F6+
+.07987+%2B+.08681+=+.16667+
+.16668+=+.16667+
Error due to rounding off, I think.
Get a 2nd opinion if needed