Aerobic Exercise A woman keeps fit by bicycling and running...

Aerobic Exercise A woman keeps fit by bicycling and running every day. On Monday she spends $\frac{1}{2} \mathrm{h}$ at each activity, covering a total of $12 \frac{1}{2} \mathrm{mi}$. On Tuesday she runs for $12 \mathrm{min}$ and cycles for $45 \mathrm{min}$, covering a total of $16 \mathrm{mi}$. Assuming that her running and cycling speeds don't change from day to day, find these speeds.

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

System of Linear Equations

This concept is used to model scenarios where there are multiple unknown variables that are related by linear equations. In problems like this, where the distances covered in different activities are provided over different time periods, the unknown speeds become the variables to solve for using simultaneous equations that stem from the distance-rate-time relationship.

Unit Conversion

When dealing with time and distance measurements in various units (e.g., minutes and hours), converting units properly ensures consistency in calculations. The ability to convert minutes to hours, for instance, is important in maintaining uniformity across the equations, which can help avoid errors in deriving the true values for the speeds.

Distance-Rate-Time Relationship

This concept involves the fundamental formula distance = rate × time, which is used to relate the speed of motion to the distance traveled over a given time period. Understanding and applying this relationship is crucial to model and solve problems involving constant speeds, such as when determining the distance covered by different activities over different time intervals.

Transcript

Please give Ace some feedback