A suspect in a high speed chase enters I-8 Eastbound at 52 miles per hour. 10 minutes later a highway patrolman enters I-8 Eastbound at the same location at 57 miles per hour. How long until the officer catches up to the suspect?

The model is $LaTeX: \displaystyle d=rt$ . The suspect has a 10 minute head start. The equation for the distance traveled by the suspect is $LaTeX: \displaystyle d=52(t + 10)$ . The highway patrolman has traveled $LaTeX: \displaystyle d=57 t$ . To catch the suspect the distances traveled must be equal. This gives the equation is $LaTeX: \displaystyle 52 t + 520=57 t$ . Solving gives that it will take $LaTeX: \displaystyle 104$ minutes to catch the suspect.