• Jul 11th 2009, 12:12 PM
Question:

A tank initally contains 60 gal of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h.

a) Find the amount of salt in the tank after t mins.
b) What is the maximum amount of salt ever in the tank?

My solution to a) is attached, but how do I find b)? I took the derivative and set it equal to zero but find no real solutions...
• Jul 11th 2009, 04:27 PM
mr fantastic
Quote:

Question:

A tank initally contains 60 gal of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h.

a) Find the amount of salt in the tank after t mins.
b) What is the maximum amount of salt ever in the tank?

My solution to a) is attached, but how do I find b)? I took the derivative and set it equal to zero but find no real solutions...

Sketch a graph of the solution (ha ha) over the domain $\displaystyle 0 \leq t \leq 60$ and look for the global maximum.

By the way, the DE should be $\displaystyle \frac{dx}{dt} = 2 - \left( \frac{3}{60 - t} \right) x$.