mixing problems: A tank initially conatins 100 gal of....

mathstresser

Junior Member
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Jan 28, 2006
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A tank initially conatins 100 gal of a salt-water solution containing .05 lb of salt for each gallon of water. At time zero, pure water is poured into the tank at a rate of 3 gal per minute. Simultaneously, a drain is opened at the bottom of the tank that allows the salt-water solution to leave the tank at a rate of 2 gal per minute. What will be the salt content in the tank when precisely 50 gal of salt solution remain?

v(0)= 100 gallons
The salt content to begin with is .05 lb/gal

The water that pours into the tank is:
3 gal/min
0 lb/gal

The water that drains out is:
2 gal/min
? lb/gal

First of all, how when does only 50 gal of salt solution remain? It starts off with 100 gallons and fills faster than it drains. Secondly, if this problem did make sense, how do we find the formula for the salt content that is draining?
rate in- rate out
rate in= 0
rate out= ?
 
you're correct ... as written, the problem doesn't make much sense.

problems like this also state that the pure water is instantaneously "mixed" with the salt solution as it is added to the tank.

just a guess, maybe the last sentence should read ...

"What will be the salt content in the tank when precisely 50 gal of salt solution is drained?
 
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