Free ACT Practice Question

In the city Xuangho, the fine for speeding on the highway is calculated in a strange manner. There is a flat fine of $\$60$ for anyone found driving above the speed limit of $100$ miles/hour and an additional fine of $\$3$ for each mile/hour if found driving above the limit of $120$ miles/hour. Lucy was fined $\$90$. At what speed (in miles/hour) was Lucy driving?