Solve each motion problem. Two trains leave a city at the...

Solve each motion problem.
Two trains leave a city at the same time. One travels north, and the other travels south $20 \mathrm{mph}$ faster. In 2 hr, the trains are 280 mi apart. Find their rates.
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Key Concepts

Rate, Distance, and Time Relationship

This concept states that the distance traveled by an object is the product of its speed (rate) and the time for which it is traveling. It is a fundamental principle in motion problems that allows the creation of equations relating these three variables, and it forms the backbone of many algebraic word problems involving movement.

Relative Motion in Opposite Directions

When two objects move away from each other in opposite directions, their separation increases at a rate equal to the sum of their individual speeds. This relative speed concept is crucial in determining how quickly the distance between the two objects changes over time.

Formulating and Solving Linear Equations from Word Problems

This concept involves translating the information provided in a word problem into one or more algebraic equations. It requires identifying the unknown variables, setting up relationships based on the problem’s conditions, and solving the resulting linear equations to find the values of the unknowns.

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