Here are three motion problems involving algebra:

Problem 1:

Two cars moving towards each other: Car A is 120 miles away from Car B. Car A is moving towards Car B at a speed of 40 miles per hour, and Car B is moving towards Car A at a speed of 30 miles per hour. How long will it take for the two cars to meet?

Problem 2:

A boat traveling upstream and downstream: A boat can travel 20 miles downstream in 2 hours, but it takes the boat 5 hours to travel the same distance upstream. What is the speed of the boat in still water and the speed of the current?

Problem 3:

A cyclist's journey: A cyclist covers a certain distance in 2 hours when traveling at 12 miles per hour. The cyclist decides to travel the same distance at a speed of 15 miles per hour. How much time will the cyclist save by traveling at the faster speed?

Would you like detailed solutions for any of these problems?

Related Questions:

1. How do you solve motion problems using algebraic equations?
2. What are some common types of motion problems in algebra?
3. How do rates of speed affect the outcome of motion problems?
4. How can we account for changes in speed or direction in algebraic motion problems?
5. How do you set up systems of equations for multiple objects in motion?

Tip: In motion problems, distance is often calculated using the formula:
$\text{Distance} = \text{Speed} \times \text{Time}.$