Systems - Girl and Sled - Newton's 3rd Law

[chipper22]

A girl of mass m_G is walking up a slippery slope while pulling a sled of unknown mass; the slope makes an angle "theta" with the horizontal. The coefficient of static friction between the girl's boots and the slope is mu_s; the friction between the sled and the slope is negligible. It turns out that the girl can pull the sled up the slope with acceleration up to "a" without slipping down the slope. Find the mass of the sled m_S. Assume that the rope connecting the girl and the sled is kept parallel to the slope at all times.

I am having trouble finding m_S, the mass of the sled. I've drawn a free body diagram of both of the systems.

 

[Doc Al]

Apply Newton's 2nd law to the entire system (girl + sled).

What forces act parallel to the slope? What force pulls the system up the slope? What's its maximum value? What's the net force?

You can also analyze the forces on the sled and girl separately and apply Newton's 2nd law to each:
What forces act on the sled? What forces act on the girl? What's the maximum value of the force pulling the girl up the slope? You'll end up with 2 equations that you can combine to solve for the mass.