Samantha ran on a fitness track for 20 min and then walked...

Samantha ran on a fitness track for 20 min and then walked for 10 min. Her running rate was 250 ft per minute faster than her walking rate. If she ran and walked a total of $15,500 \mathrm{ft},$ how fast did she run?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Translating Word Problems into Algebraic Equations

This concept involves reading a word problem carefully, assigning variables to unknown quantities, and then setting up equations based on the relationships described. This technique is crucial for turning real-world scenarios into solvable mathematical problems.

Solving Linear Equations

Once an appropriate equation is formed, solving a linear equation involves combining like terms, isolating the variable, and performing arithmetic operations to find the solution. This systematic procedure is essential for finding unknown quantities in problems that can be modeled linearly.

Distance = Rate × Time

This principle is used to calculate the distance traveled by any moving object when its speed (rate) and the time of motion are known. It is foundational in problems involving constant rates where distance is computed as the product of rate and time.

Transcript

Please give Ace some feedback