A suspect in a high speed chase enters I-8 Eastbound at 59 miles per hour. 27 minutes later a highway patrolman enters I-8 Eastbound at the same location at 68 miles per hour. How long until the officer catches up to the suspect?

The model is $LaTeX: \displaystyle d=rt$ . The suspect has a 27 minute head start. The equation for the distance traveled by the suspect is $LaTeX: \displaystyle d=59(t + 27)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=68 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 59 t + 1593=68 t$ . Solving gives that it will take $LaTeX: \displaystyle 177$ minutes to catch the suspect.