A suspect in a high speed chase enters I-8 Eastbound at 67 miles per hour. 55 minutes later a highway patrolman enters I-8 Eastbound at the same location at 78 miles per hour. How long until the officer catches up to the suspect?

The model is $LaTeX: \displaystyle d=rt$ . The suspect has a 55 minute head start. The equation for the distance traveled by the suspect is $LaTeX: \displaystyle d=67(t + 55)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=78 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 67 t + 3685=78 t$ . Solving gives that it will take $LaTeX: \displaystyle 335$ minutes to catch the suspect.