A suspect in a high speed chase enters I-8 Eastbound at 82 miles per hour. 6 minutes later a highway patrolman enters I-8 Eastbound at the same location at 85 miles per hour. How long until the officer catches up to the suspect?

The model is $LaTeX: \displaystyle d=rt$ . The suspect has a 6 minute head start. The equation for the distance traveled by the suspect is $LaTeX: \displaystyle d=82(t + 6)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=85 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 82 t + 492=85 t$ . Solving gives that it will take $LaTeX: \displaystyle 164$ minutes to catch the suspect.