### 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 7 hours later. She walks at a constant rate of 40/3 miles per hour. How long will it take for Carrie to catch up with Bud and how far will she have walked by then?

$$y=4(x+7)\textrm{ },\textrm{ }y=\frac{40}{3} \times x$$

2.

Antonio is riding on a train. He gets up from his seat and walks forward. As he walks, he travels 61/30 miles in 2 minutes. As he walks back to his seat, he travels 53/30 miles in 2 minutes. How fast was the train moving, and how fast did Antonio walk inside the train (both in miles per hour)?

$$\frac{2}{60} \times (x+y)=\frac{61}{30}\textrm{ },\textrm{ }\frac{2}{60} \times (x-y)=\frac{53}{30}$$

3.

Alan has challenged Sam to a duel with water pistols at 200 feet. They start walking in opposite directions. Alan walks at 6 feet per second. Sam runs at 14 feet per second. How long will it take them to be 200 feet apart?

$$(6+14)x=200$$