Jose drove 15 miles to pick up his sister and then returned...

Jose drove 15 miles to pick up his sister and then returned home. On the return trip, he was able to average 15 miles per hour faster than he did on the trip to pick her up. If the total trip took 1 hour, then what was
Jose's average speed on the return trip?

Key Concepts

Distance-Rate-Time Relationship

This concept is fundamental in motion problems and states that distance equals rate multiplied by time. It forms the basis for setting up equations in scenarios involving movement, where knowing any two of the three variables allows for solving the third. It is widely applied in problems that require determining time taken for particular journey segments based on speeds and distances.

Average Speed Calculation

The idea of average speed is crucial when different segments of a trip are traveled at varying speeds. It is defined as the total distance traveled divided by the total time taken. This concept helps in analyzing overall performance in journey problems and is essential when the speeds vary over different parts of the journey.

Forming and Solving Equations

In many motion problems, the distances, speeds, and times for different parts of the trip are related through equations. Formulating these equations and solving them systematically allows for the determination of unknown quantities. It is a key concept in algebra that helps in breaking down complex problems into manageable parts.

Quadratic Equations

Often, the equations that arise from motion problems lead to quadratic equations. Solving these involves identifying the correct standard form and applying methods such as factoring, completing the square, or the quadratic formula. This concept is central to algebra and helps in finding meaningful solutions in problems where linear equations are insufficient.

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