Solve each motion problem. Two planes leave an airport at...

Solve each motion problem.
Two planes leave an airport at the same time, one flying east, the other flying west. The eastbound plane travels 150 mph slower. They are $2250 \mathrm{mi}$ apart after 3 hr. Find the rate of each plane.
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Key Concepts

Distance-Rate-Time Relationship

This fundamental concept states that distance is the product of speed (rate) and time. It provides the basis for setting up the equation to relate the travel times and speeds of moving objects, and it is essential for solving motion problems.

Relative Motion in Opposite Directions

When two objects travel in opposite directions, the distance between them increases at a rate equal to the sum of their individual speeds. This concept is used to determine how far apart they will be after a given time.

Algebraic Equation Setup

This involves defining variables to represent unknown quantities and forming equations based on the relationships provided by the problem. Setting up the correct algebraic equation is critical to solving for unknown speeds or distances in motion problems.

Solving Linear Equations

Once the equation is established, the process of solving linear equations involves isolating the variable using inverse operations. This step-by-step methodology is key to finding the numerical values of the unknown quantities.

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