Physics, please check my work

I've posted a couple questions tonight, I missed a couple classes recently due to forces out of my control and I really want to learn and understand how to do this. Thank you to everyone who has assisted for taking the time to look over my work and correct it as needed. I apologize in advance if I mess this one up too. I'm really beat but I want to finish this up before I go to bed tonight.

Two rats are fighting over a hunk of cheese (m=10kg). The cheese slides to the right at a constant speed if rat 1 pulls to the left 230N and rat 2 pulls to the right 350N. What is the cheese's coefficient of kinetic friction on the floor?

Here's what I have:
Find a: a=Fnet/m (Fnet=120N m=10kg) a=120N/10kg a=12m/s^2

Find N: N=mg (m=10kg g=9.8) N=10 x 9.8 N=98

Find fk: fk=ma (m=10kg a=12m/s^2) fk=10 x 12 fk=120

last uk=fk/N uk=(ma)/(mg) *m's cancel out* uk=a/g uk=12/9.8 uk= 1.22449

Please check and see if I did this right or totally messed it up. Oh, does the cheese sliding have anything to do with any of the equations?
Thanks

You have the right answer.

Technically you should say that a = 0 and Fnet = 350 - 230 - fk
But the math is the same the way you wrote it.

Whether the cheese is sliding or still makes no difference. It is the (lack of) acceleration that matters. If the cheese were still, the friction would be static rather than kinetic.