A passenger train and a freight train leave cities 400 miles...

Name: Problem 95, Chapter 3: Beginning and Intermediate Algebra
Uploaded: 2021-03-23T14:59:11-08:00
Duration: 6 min 9 s
Channel: Ruby P
Description: A passenger train and a freight train leave cities 400 miles apart and travel toward each other. The passenger train is traveling 20 mph faster than the freight train. Find the speed of each train if they pass each other after 5 hours.

A passenger train and a freight train leave cities 400 miles apart and travel toward each other. The passenger train is traveling 20 mph faster than the freight train. Find the speed of each train if they pass each other after 5 hours.

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Key Concepts

Setting up Equations

Setting up equations involves translating a word problem into mathematical expressions by assigning variables to the unknowns and creating relationships based on the facts provided. This method is used to organize the information given about speeds, time, and distance into solvable equations.

Solving Systems of Equations

Solving systems of equations entails finding the values of multiple unknown variables that satisfy all the given equations simultaneously. In problems where multiple relationships interconnect, such as differences in speeds and combined distances, this approach is key to reaching the solution.

Uniform Motion

Uniform motion refers to the principle that distance traveled is the product of speed and time. This concept is fundamental in solving motion problems, as it allows one to model an object's movement with the equation distance = speed × time.

Relative Speed

Relative speed is the concept that when two objects move towards each other, the rate at which the gap between them closes is the sum of their individual speeds. This idea is essential for determining how quickly two objects will meet when they start from different points.

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