Here are three algebraic motion problems:

### 1. Distance-Speed-Time Problem
A car travels 150 miles at a constant speed. If the speed of the car was 10 mph faster, it would take 1 hour less to cover the same distance. What is the car's original speed?

### 2. Relative Motion Problem
Two trains leave from two different cities at the same time and travel toward each other. The first train is traveling at 60 mph, and the second train is traveling at 80 mph. The distance between the cities is 420 miles. How long will it take for the two trains to meet?

### 3. Downstream-Upstream Motion Problem
A boat travels 36 miles downstream in 3 hours. It takes 4.5 hours to travel the same distance upstream. What is the speed of the current and the speed of the boat in still water?

---

Would you like a detailed solution for any of these?  
Here are 5 related questions to challenge you further:

1. What happens to the time if the speed of a vehicle doubles while covering the same distance?
2. How do you set up equations to solve for two unknown speeds in relative motion problems?
3. How would you adjust the problem if the speed of the second train was reduced by 20 mph?
4. Can you think of any scenarios where speed and time change inversely?
5. How does the current affect a boat's speed when moving upstream vs. downstream?

**Tip:** In motion problems, the key formula to remember is \( \text{Distance} = \text{Speed} \times \text{Time} \).

Explore 3 classic algebra motion problems involving distance, speed, and time. These problems include determining original speed, calculating time for two trains to meet, and solving for boat and current speeds. Ideal for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation