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Questions: Algebra BusinessCalculus
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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 \(\displaystyle d=rt\). The suspect has a 27 minute head start. The equation for the distance traveled by the suspect is \(\displaystyle d=59(t + 27)\). The highway patrolman has traveled \(\displaystyle d=68 t\). To catch the suspect the distances traveled must be equal. This gives the equation is \(\displaystyle 59 t + 1593=68 t\). Solving gives that it will take \(\displaystyle 177\) minutes to catch the suspect.
\begin{question}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?
\soln{10cm}{The model is $d=rt$. The suspect has a 27 minute head start. The equation for the distance traveled by the suspect is $d=59(t + 27)$. The highway patrolman has traveled $d=68 t$. To catch the suspect the distances traveled must be equal. This gives the equation is $59 t + 1593=68 t$. Solving gives that it will take $177$ minutes to catch the suspect. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>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?</p> </p>
<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 27 minute head start. The equation for the distance traveled by the suspect is <img class="equation_image" title=" \displaystyle d=59(t + 27) " src="/equation_images/%20%5Cdisplaystyle%20d%3D59%28t%20%2B%2027%29%20" alt="LaTeX: \displaystyle d=59(t + 27) " data-equation-content=" \displaystyle d=59(t + 27) " /> . The highway patrolman has traveled <img class="equation_image" title=" \displaystyle d=68 t " src="/equation_images/%20%5Cdisplaystyle%20d%3D68%20t%20" alt="LaTeX: \displaystyle d=68 t " data-equation-content=" \displaystyle d=68 t " /> . To catch the suspect the distances traveled must be equal. This gives the equation is <img class="equation_image" title=" \displaystyle 59 t + 1593=68 t " src="/equation_images/%20%5Cdisplaystyle%2059%20t%20%2B%201593%3D68%20t%20" alt="LaTeX: \displaystyle 59 t + 1593=68 t " data-equation-content=" \displaystyle 59 t + 1593=68 t " /> . Solving gives that it will take <img class="equation_image" title=" \displaystyle 177 " src="/equation_images/%20%5Cdisplaystyle%20177%20" alt="LaTeX: \displaystyle 177 " data-equation-content=" \displaystyle 177 " /> minutes to catch the suspect. </p> </p>