Problem With Cylinder Involving Mass and Volume

[The James]

Homework Statement

There is a cylinder with two sections (not straight down the middle). One has density 4.5(g/cm^3) the other with 6.4. The radius of the cylinder is 6cm and the total length is 19cm. The total mass is 11833 grams. I need to find the length of the lighter density section of the cylinder.

Homework Equations

A of circle = pi*r^2
V = B*h
D = m/v

The Attempt at a Solution

I could easily solve this problem if I knew the steps to take. The total volume is about 113 cm^3, but I don't see how I can apply that information. Also, am I correct in thinking that densities cannot be combined? Sorry for the measly attempt, it is just that I am unable to find a way to solve this. The math should be easy. I just need a plan.

 

[CWatters]

You can write plenty of equations. For example write equations for ...

1) The mass of the low density part M_LD as a function of it's unknown length L_LD
2) The mass of the high density part M_HD as a function of it's unknown length L_HD

You can also write v.simple equations such as ones for..

3) The total mass M_TOTas a function of M_LD and M_HD
4) The total Length L_TOT as a function of L_LD and L_HD

Then you will have lots of equations and some unknowns. Solve.