You are a highway patrol officer monitoring traffic with a radar gun on a curvy section of Highway 1. The posted speed limit is 45 miles per hour (mph). A car passes and you see it is traveling 68 mph.

When you hop on your bike to pull the car over, however, the motorcycle won’t start. You try again and again, worried that you won’t be able to catch Speedy McSpeedster before he can turn off the highway. Finally, your bike starts and you begin your pursuit 30 seconds after the speeding car has passed you on the roadside. The next exit is 3.6 miles up the road.

How fast do you need to go to catch up to the speeding car before it reaches the exit?