# Thread: Mixtures type word problem

1. ## Mixtures type word problem

50 g of a certain chemical is added to 200mL of water; the chemical dissolves in water at a rate proportional to the product of the amount of undissolved chemical and the difference between concentrations in a saturated solution and the existing concentration in the solution. A saturated solution contains 25g of chemical in 100mL of solution.

(a) Show that the differential equation that describes the situation is,

$\frac{dx}{dt} = \frac{k}{200}(50-x)^{2}, x(0) = 0$

where x(t) is the number of grams of dissolved chemical at time t.

These word problems always cause me trouble. The question seems so complicated I don't even know what to start with.

Can someone help me get started?

2. breaking down and translating the problem statement (hope you're not color blind) ...

the chemical dissolves in water at a rate proportional to the product of the amount of undissolved chemical and the difference between concentrations in a saturated solution and the existing concentration in the solution.
dx/dt = k(50-x)(25/100 - x/200)

if you put that together and you'll get the desired DE