Why do neutrons have spin? are quarks responsible?

Before I go in to my question I would like to mention I am 15 and though I am quite knowledgeable I'd like it very much if these answers were in layman's terms although I understand that may be difficult because of the nature of my topic. As far I understand it quantum spin is the property held by all particles by which through angular momentum they have a magnetic field which is usually categorised as spin up or spin down. This was originally believed to be because of charged particles rotating and thus creating magnetism. ( like an electromagnet ie. motion plus charge equals magnetism) this was discarded because of neutral particles such as neutrons. I,after reading this, began to wonder how that could be when all hadrons are made up of quarks (which are charged) so why couldn't their spin (the quarks spin) be responsible for the neutrons (like in a permanent magnet lots of charged particles 'working together' to create one magnetic field) I was then informed that due to the fact that a quarks spin is 1/2 and as is a neutrons this is impossible as surely the three quarks spins would add up to 3/2. Now I had accepted this (although looking at it now I am not sure how well informed that person was) until I saw a car today and realised that if all 4 wheels travels at 30 mph the cars total speed isn't 120 mph it is still 30mph. so why couldn't this principle apply to the quarks spin and the hadrons? Could someone explain that to me? Am I just greatly misinformed? Why do neutrons have spin? Is it anything to do with quarks?