Leadfoot Lilly was driving miles per hour when she passed a parked highway patrol car. By the time she was half a mile past the spot where the patrol car was parked, the officer was driving after her at miles per hour. If these rates remain constant, how long will it take the officer to catch up to Lilly? Write and solve an equation to represent this situation.
You can assume the officer did not move while accelerating to 100 mph.