DE: Unit Cancellations Not Making sense

[dillonmhudson]

Homework Statement

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Homework Equations

$$\frac{dQ}{dt}$$=rate in - rate out

The Attempt at a Solution

Why the heck do they cancel units incorrectly?

 

[Dick]

Hard to say until you tell us what the heck Q is.

 

[dillonmhudson]

Q is the amount of dye in the tank.
dQ is the rate of change of the amount of dye in the tank.

 

[Dick]

Q is the amount of dye in the tank.
dQ is the rate of change of the amount of dye in the tank.

Then all the terms in your equation should have units of grams of dye per minute. I think the Q/100 l/min should be g/min. Probably a typo.

 

[dillonmhudson]

Ok that's what I was hoping - thank you.