A suspect in a high speed chase enters I-8 Eastbound at 71 miles per hour. 22 minutes later a highway patrolman enters I-8 Eastbound at the same location at 82 miles per hour. How long until the officer catches up to the suspect?

The model is $LaTeX: \displaystyle d=rt$ . The suspect has a 22 minute head start. The equation for the distance traveled by the suspect is $LaTeX: \displaystyle d=71(t + 22)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=82 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 71 t + 1562=82 t$ . Solving gives that it will take $LaTeX: \displaystyle 142$ minutes to catch the suspect.