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A suspect in a high speed chase enters I-8 Eastbound at 73 miles per hour. 40 minutes later a highway patrolman enters I-8 Eastbound at the same location at 81 miles per hour. How long until the officer catches up to the suspect?

The model is \(\displaystyle d=rt\). The suspect has a 40 minute head start. The equation for the distance traveled by the suspect is \(\displaystyle d=73(t + 40)\). The highway patrolman has traveled \(\displaystyle d=81 t\). To catch the suspect the distances traveled must be equal. This gives the equation is \(\displaystyle 73 t + 2920=81 t\). Solving gives that it will take \(\displaystyle 365\) minutes to catch the suspect.

Download \(\LaTeX\) 

\begin{question}A suspect in a high speed chase enters I-8 Eastbound at 73 miles per hour. 40 minutes later a highway patrolman enters I-8 Eastbound at the same location at 81 miles per hour.  How long until the officer catches up to the suspect?
    \soln{10cm}{The model is $d=rt$.  The suspect has a 40 minute head start. The equation for the distance traveled by the suspect is $d=73(t + 40)$. The highway patrolman has traveled $d=81 t$. To catch the suspect the distances traveled must be equal. This gives the equation is $73 t + 2920=81 t$. Solving gives that it will take $365$ minutes to catch the suspect. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>A suspect in a high speed chase enters I-8 Eastbound at 73 miles per hour. 40 minutes later a highway patrolman enters I-8 Eastbound at the same location at 81 miles per hour.  How long until the officer catches up to the suspect?</p> </p>
HTML for Canvas
<p> <p>The model is  <img class="equation_image" title=" \displaystyle d=rt " src="/equation_images/%20%5Cdisplaystyle%20d%3Drt%20" alt="LaTeX:  \displaystyle d=rt " data-equation-content=" \displaystyle d=rt " /> .  The suspect has a 40 minute head start. The equation for the distance traveled by the suspect is  <img class="equation_image" title=" \displaystyle d=73(t + 40) " src="/equation_images/%20%5Cdisplaystyle%20d%3D73%28t%20%2B%2040%29%20" alt="LaTeX:  \displaystyle d=73(t + 40) " data-equation-content=" \displaystyle d=73(t + 40) " /> . The highway patrolman has traveled  <img class="equation_image" title=" \displaystyle d=81 t " src="/equation_images/%20%5Cdisplaystyle%20d%3D81%20t%20" alt="LaTeX:  \displaystyle d=81 t " data-equation-content=" \displaystyle d=81 t " /> . To catch the suspect the distances traveled must be equal. This gives the equation is  <img class="equation_image" title=" \displaystyle 73 t + 2920=81 t " src="/equation_images/%20%5Cdisplaystyle%2073%20t%20%2B%202920%3D81%20t%20" alt="LaTeX:  \displaystyle 73 t + 2920=81 t " data-equation-content=" \displaystyle 73 t + 2920=81 t " /> . Solving gives that it will take  <img class="equation_image" title=" \displaystyle 365 " src="/equation_images/%20%5Cdisplaystyle%20365%20" alt="LaTeX:  \displaystyle 365 " data-equation-content=" \displaystyle 365 " />  minutes to catch the suspect. </p> </p>