If someone hit my car and agreed to pay but hasn't how long do i have?

I suggest contacting you insurance company. But if you don't have their name and phone number don't bother because you can't contact them. Hope i can help you out of your dilemma. Further suggestion Send them a registered letter asking for payment for your damages, include a estimate for repair. If they don't pay you take them to small claims court to recover your damages. Make sure when you go to court that you have a copy of your letter, estimates, photos of your car, accident report, and any other data you consider important.