John bikes a distance of 120 miles and then returns over the...

Name: Problem 62, Chapter 0: Applied Calculus For Business, Economics, and Finance
Uploaded: 2021-05-15T08:22:59-08:00
Duration: 2 min 36 s
Channel: Wendi Zhao
Description: John bikes a distance of 120 miles and then returns over the same route. On his return his average speed is 2 miles per hour more than when going. If the combined time for both trips was 22 hours, what was his speed each way?

John bikes a distance of 120 miles and then returns over the same route. On his return his average speed is 2 miles per hour more than when going. If the combined time for both trips was 22 hours, what was his speed each way?

Key Concepts

Uniform Motion

Uniform motion problems involve the relationship between distance, speed, and time, typically expressed with the equation time = distance/speed. This foundational concept allows for the analysis of travel situations by determining one variable when the other two are known, making it essential for solving problems involving constant speeds over fixed distances.

Algebraic Modeling

Algebraic modeling is the process of translating real-world scenarios into mathematical equations using variables. In travel problems, this involves representing unknown speeds, times, or distances with symbols and expressing the relationships between them, enabling systematic problem-solving through the use of equations.

Quadratic Equations

Quadratic equations often arise in algebraic problems when multiple relationships are modeled together, such as in travel problems where the total time or distance leads to a product or square of an unknown variable. Solving these equations—through factoring, completing the square, or the quadratic formula—is a key step in finding valid solutions to the problem.

System of Equations

Systems of equations consist of multiple equations that must be solved simultaneously to find the values of the unknown variables. In scenarios where different segments of a journey have distinct speeds or times, setting up and solving a system of equations is crucial to account for all conditions and arrive at a consistent solution.

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