Algebra 28 - Solving Motion Problems with Linear Equations

TL;DR

Linear equations can be used to solve real-world problems involving speed, time, and distance.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. In the last lecture we saw how linear equations can be used to solve real-world problems involving quantities such as ages and dimensions. In this lecture, we will see how to use linear equations to solve problems involving time, distance, and speed. Most of us are familiar with the concept o... Read More

Key Insights

• 🐎 Linear equations can be used to solve problems involving speed, time, and distance.
• 💱 Speed is determined by the change in distance over the change in time.
• ⌛ The formula "speed times time equals distance" is a useful tool in solving these problems.
• 😫 By assigning variables and setting up equations, unknown values for speed, time, and distance can be determined.
• 🚙 Linear equations can handle situations with a single vehicle or multiple vehicles with different speeds.
• 🐎 The relationship between speed, time, and distance remains consistent in linear equations.
• 🍉 Solving linear equations involves simplifying, distributing, and canceling terms to find the unknown variable.

Questions & Answers

Q: How can linear equations be used to solve problems involving speed, time, and distance?

Linear equations can be created using the formula "speed times time equals distance" and solved to find the unknown variable (speed, time, or distance). By substituting the known values, the unknown value can be determined.

Q: Can linear equations be used to solve problems involving multiple vehicles with different speeds?

Yes, by representing the speeds of the vehicles with variables, equations can be formed with the distances traveled by each vehicle and the total distance. Solving these equations will yield the speeds of the vehicles.

Q: How can linear equations help determine the time spent traveling at different speeds?

By assigning variables to represent the times spent at different speeds, equations can be set up using the formula "distance equals speed times time." Solving these equations will provide the values for the time spent at each speed.

Q: What is the relationship between speed, time, and distance in linear equations?

The relationship is represented by the formula "speed times time equals distance." This equation can be rearranged to solve for any of the three variables if the values for the others are known.

Summary & Key Takeaways

• Linear equations can be used to solve problems involving time, distance, and speed.

• Speed is defined as the change in distance over the change in time.

• By using the formula "speed times time equals distance," any of the three quantities can be calculated if the values of the other two are known.