Hey. My book is being a really bad teacher right now so I went on google for some help and I got this:

http://college.cengage.com/mathemati...lc7eap1502.pdf
The linear ODE stuff makes sense, but I'm stuck on setting up a differential equation (the one on page 5). It says:

A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing 50% water and 50% alcohol is added to the tank at the rate of 4 gallons per minute. As the second solution is being added, the tank is being drained at the rate of 5 gallons per minute. Assuming the solution in the tank is stirred constantly, how much alcohol is in the tank after 10 minutes?

Solution: Let y be the number of gallons of alcohol in the tank at any time t. You know that y = 5 when t = 0. Because the number of gallons of solution in the tank at any time is 50 - t and the tank loses 5 gallons of solution per minute, it must lose

$\displaystyle \frac{5}{50-t}y$

gallons of alcohol per minute.

Ok. I'm having a problem understanding the 50 - t. Shouldn't it be 50 - 5t??

Thanks in advance!