Tuesday

October 21, 2014

October 21, 2014

Posted by **COFFEE** on Friday, July 13, 2007 at 4:36pm.

A tank initially contains 80 gallons of fresh water. A 10% acid solution flows into the tank at the rate of 3 gallons per minute. The well-stirred mixture flows out of the tank at the rate of 3 gallons per minute. Find the amount of acid in the tank at the end of any time t. How much acid will be in the tank in 30 minutes? What will be the concentration (%) of acid in the tank after 30 minutes?

solution=0.3 gallons acid + 2.7 gallons H20

dy/dt = (rate in) - (rate out)

rate in = (0.3)(3) = 0.9 gallons/min

<-would this be gallons per min?

rate out = ((y(t))/80) * 3 gal/min

rate out = y(t)/(80/3)

dy/dt=(0.9)-(y(t))/(80/3)

dy/dy=((773/30)-y(t))/(80/3)

Seperate into two intergrals:

Integral(dy/((773/30)-y)=Integral(dt/(80/3))

-ln|(773/30)-y| = 3t/80+C, C=-ln|773/30|

-ln|(773/30)-y|=3t/80 - ln|773/30|

y(t)=(773/30)-(773/30)e^(-3t/80)

Is this the correct equation?

Then at 30 minutes, y(30) would be 17.4 gallons acid

Percentage after 30 minutes=17.4/80

=21.8% acid???

Thanks.

correct procedure, however, one question: how did you get rate in .3*3? Wasn't it ten percent?

ah yes. Thank you!

**Answer this Question**

**Related Questions**

math - Water is Pumped into an underground tank at a constant rate of 8 gallons ...

maths - 1)a linear function is represented by f(x)=2x+7 which of the following ...

math - An inverted square pyramid has a height equal to 8m and a top edge to 3m...

math - Tank 1 initial contains 70 L (liters) of water and 450 g of salt, while ...

math - A tank contains 50 gallons of a solution composed of 90% water and 10% ...

calculus - Water is Pumped into an underground tank at a constant rate of 8 ...

Calculus - A tank contains 2920 L of pure water. A solution that contains 001 kg...

calculus - A water heater in the shape of a circular cylinder is standing ...

maths - 3.An 1145 L tank contains 295 L of water and is being filled with brine ...

Grenada - John has a 25-gallon fish tank. John filled his tank today with 23-...