Can't mop my floors clean?

I've been staying in an apartment provided to me by some family members that own it. When I moved in I noticed that the kitchen floors have been very dingy and dirty looking. I have tried to mop it up but the dirt just smears and the linoleum is textured so the dirt really sticks to it. One of the family members recently snuck into my apartment while I was away and us now claiming that I have made the floors dirty and has threatned to kick me out. I'm at a loss of what more I can do. Anyone know any tricks thatcan help?