A suspect in a high speed chase enters I-8 Eastbound at 81 miles per hour. 6 minutes later a highway patrolman enters I-8 Eastbound at the same location at 84 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 $LaTeX: \displaystyle d=81(t + 6)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=84 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 81 t + 486=84 t$ . Solving gives that it will take $LaTeX: \displaystyle 162$ minutes to catch the suspect.