This document discusses solving motion problems using linear equations. It provides an example problem where two cars that were originally 450 miles apart traveled toward each other and met after 5 hours. One car traveled twice as fast as the other. The problem is solved by assigning variables to represent the speeds of each car, writing an equation to represent the relationship between distance, rate, and time, and solving to determine the speeds of each car.

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Applications and Modeling with
Linear Equations1.2
• Solving Applied Problems
• Geometry Problems
• Motion Problems
• Mixture Problems
• Modeling with Linear Equations

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Motion Problems
Problem-Solving Hint In a motion
problem, the components distance, rate,
and time are denoted by the letters d, r,
and t, respectively. (The rate is also called
the speed or velocity. Here, rate is
understood to be constant.)
d rt and its related forms
d
r
t
 and
d
t
r


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Example 2 SOLVING A MOTION PROBLEM
Two cars that were 450 miles apart traveled
toward each other. They met after 5 hours.
If one car traveled twice as fast as the
other, what were their speeds?
Solution
Step 1 Read the problem.

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Example 2 SOLVING A MOTION PROBLEM
Step 2 Assign a variable.
Two cars that were 450 miles apart traveled toward each other.
They met after 5 hours. If one car traveled twice as fast as the
other, what were their speeds?

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Example 2 SOLVING A MOTION PROBLEM
Step 2 Assign a variable.
Two cars that were 450 miles apart traveled toward each other.
They met after 5 hours. If one car traveled twice as fast as the other,
what were their speeds?

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Example 2 SOLVING A MOTION PROBLEM
Step 3 Write an equation.

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Example 2 SOLVING A MOTION PROBLEM
Step 4 Solve.

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Example 2 SOLVING A MOTION PROBLEM
Step 5 State the answer.
Step 6 Check.