3 car accident car was pushed in to me by speeding driver who has no insurance will middle car who was pushed into me insurance cover repairs to my car?

If you have collision coverage on your policy insist that your insurance company pay to repair your car, subject to your deductible. This will guarantee a couple of things:

1. The repairs are done quickly.

2. Most insurance companies will guarantee the repairs for the life of the vehicle. So if something goes wrong down the road, you'll be able to deal with your own company.

3. Your insurance company will seek to recover their payout as well as your deductible through a process called subrogation.

If you do not have collision coverage then you can ask the middle car (the one immediately behind you) to pay for the damage. Technically this car was stopped too close to you and had they given more distance they would not have hit you.

If neither of these solutions work, then you should obtain an attorney and sue the speeder. Any time you are not At Fault in a car accident you should definitely seek out legal counsel. The primary reason you purchase insurance is to protect you from financial catastrophe when you are at fault. Car insurance is really not designed for you when you are not at fault.