This is a somewhat challenging problem from the 1997 American Invitational Mathematics Exam (AIME).

“A car travels due east at 2/3 miles per minute on a long, straight road. At the same time, a circular storm, whose radius is 51 miles, moves southeast at √2/2 miles per minute. At time *t* = 0, the center of the storm is 110 miles due north of the car. At time *t = t*_{1} minutes, the car enters the storm circle, and at time *t = t*_{2} minutes, the car leaves the storm circle. Find (*t*_{1} + *t*_{2})/2.”

See the Storm Chaser Problem