### 8.6 Motion Problems

Problem #

Problem Statement

Problems Similar To

1.

Bud takes a leisurely stroll. He walks at a constant rate of 3 miles per hour. Carrie starts out for a brisk walk 5 hours later. She walks at a constant rate of 21/2 miles per hour. How long will it take for Carrie to catch up with Bud and how far will she have walked by then?

$$y=3(x+5)\textrm{ },\textrm{ }y=\frac{21}{2} \times x$$

2.

Antonio is riding on a train. He gets up from his seat and walks forward. As he walks, he travels 109/30 miles in 2 minutes. As he walks back to his seat, he travels 33/10 miles in 2 minutes. How fast was the train moving, and how fast did Antonio walk inside the train (both in miles per hour)?

$$\frac{2}{60} \times (x+y)=\frac{109}{30}\textrm{ },\textrm{ }\frac{2}{60} \times (x-y)=\frac{33}{10}$$

3.

Alan has challenged Sam to a duel with water pistols at 72 feet. They start walking in opposite directions. Alan walks at 9 feet per second. Sam runs at 15 feet per second. How long will it take them to be 72 feet apart?

$$(9+15)x=72$$