Shooting backwards, the arrow would have a 90MPH tailwind. So add that to the speed that it leaves the bow at, and you (might) get 180MPH.
I say "might" for several reasons:
1. Arrows are drag-stabilised projectiles. A tailwind that strong could stuff up the drag stabilisation.
2. There'll be a load of turbulence from the backwash of the car. Results unpredictable -- turbulence has baffled some of the best minds.
3. The arrow won't necessarily catch all the force of the tailwind, so it could be a lot slower than 180MPH.
Hmm, only one way top settle this...
But not on the M62 please when there's a red Renault Clio behind you!