# DE: Unit Cancellations Not Making sense

1. ### dillonmhudson

50
1. The problem statement, all variables and given/known data
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.

2. Relevant equations
$$\frac{dQ}{dt}$$=rate in - rate out

3. The attempt at a solution
Why the heck do they cancel units incorrectly?

2. ### Dick

25,913
Hard to say until you tell us what the heck Q is.

3. ### dillonmhudson

50
Q is the amount of dye in the tank.
dQ is the rate of change of the amount of dye in the tank.

4. ### Dick

25,913
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.

5. ### dillonmhudson

50
Ok that's what I was hoping - thank you.