### 8.6 Motion Problems

Problem #

Problem Statement

Problems Similar To

1.

Bud takes a leisurely stroll. He walks at a constant rate of 4 miles per hour. Carrie starts out for a brisk walk 5 hours later. She walks at a constant rate of 8 miles per hour. How long will it take for Carrie to catch up with Bud and how far will she have walked by then?

\begin{equation}y=4(x+5)\textrm{ },\textrm{ }y=8x\end{equation}

2.

Antonio is riding on a train. He gets up from his seat and walks forward. As he walks, he travels 38/15 miles in 2 minutes. As he walks back to his seat, he travels 7/3 miles in 2 minutes. How fast was the train moving, and how fast did Antonio walk inside the train (both in miles per hour)?

\begin{equation}\frac{2}{60} \times (x+y)=\frac{38}{15}\textrm{ },\textrm{ }\frac{2}{60} \times (x-y)=\frac{7}{3}\end{equation}

3.

Alan has challenged Sam to a duel with water pistols at 210 feet. They start walking in opposite directions. Alan walks at 9 feet per second. Sam runs at 12 feet per second. How long will it take them to be 210 feet apart?

\begin{equation}(9+12)x=210\end{equation}