At time 0, Car A is travelling at 100 miles per hour and Car B is travelling at 20 miles per hour. One minute later, Car A is travelling at 80 miles per hour and Car B is travelling at 100 miles per hour. Show that there is a moment during that minute where Cars A and B are travelling at the exact same speed. (Note: We assume that the speed of a car is a continuous function of time.)

using intermediate value theorem