### 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 6 hours later. She walks at a constant rate of 10 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+6)\textrm{ },\textrm{ }y=10x\end{equation}

2.

Antonio is riding on a train. He gets up from his seat and walks forward. As he walks, he travels 133/30 miles in 2 minutes. As he walks back to his seat, he travels 127/30 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{133}{30}\textrm{ },\textrm{ }\frac{2}{60} \times (x-y)=\frac{127}{30}\end{equation}

3.

Alan has challenged Sam to a duel with water pistols at 144 feet. They start walking in opposite directions. Alan walks at 4 feet per second. Sam runs at 14 feet per second. How long will it take them to be 144 feet apart?

\begin{equation}(4+14)x=144\end{equation}