SOLUTION: A tank is filled in 9 hrs. and drained in 11 hrs. How long will it take to fill the tank if the drain is left half open.

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Question 886043: A tank is filled in 9 hrs. and drained in 11 hrs. How long will it take to fill the tank if the drain is left half open.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A tank is filled in 9 hrs. 

So the fill rate is 1 tank per 9 hrs or

matrix%281%2C2%2C1%2Ctank%29%2Fmatrix%281%2C2%2C9%2Chrs%29 or matrix%281%2C2%2C1%2F9%2Ctank%2Fhr%29,

and the drain rate is -1 tank per 11 hrs or

matrix%281%2C2%2C-1%2Ctank%29%2Fmatrix%281%2C2%2C11%2Chrs%29 or matrix%281%2C2%2C-1%2F11%2Ctank%2Fhr%29.

Since the drain is only half open, it's rate is halved

matrix%281%2C2%2Cexpr%281%2F2%29%2A%28-1%2F11%29%2Ctank%2Fhr%29 or matrix%281%2C2%2C-1%2F22%2Ctank%2Fhr%29

Their combined rate is matrix%281%2C2%2C1%2F9-1%2F22%2Ctank%2Fhr%29 or

since 1%2F9-1%2F22=22%2F198-9%2F198=13%2F198

their combined fill rate is matrix%281%2C2%2C13%2F198%2Ctank%2Fhr%29

Suppose it takes x hours.  Then

matrix%281%2C2%2C13%2F198%2Ctank%2Fhr%29%22%22%2A%22%22matrix%281%2C2%2Cx%2Chr%29 %22%22=%22%22 matrix%281%2C2%2C1%2Ctank%29

expr%2813%2F198%29%2Ax%22%22=%22%221

x%22%22=%22%22198%2F13%22%22=%22%22matrix%281%2C2%2C15%263%2F13%2Chours%29 

Edwin