6.5 Applying Systems DAY 2: Rate Problems

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6.5 Applying SystemsDAY 2 Rate Problems

• Algebra 9.0, 15.0

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Solving System Word Problems

• Systems can be used to solve complex word
  problems that involve two or more variables.
• To solve a word problem
• Identify important information
• (underline or circle)
• 2) Build the two linear equations
• (use x, y, and important numbers)
• 3) Determine which method to solve the system
• (graph, substitute, eliminate)

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Rate Problems

• You can use a table to set up a rate problem.
• Rate problems use the formula D rt
• Distance Rate x Time
• Rate equations involve two directions upstream
  and downstream, or headwind and tailwind.
• Upstream and headwind slow the rate down
• Downstream and tailwind speed the rate up
• x usually represents the rate of the person or
  vehicle
• y usually represents the rate of the wind or
  water.

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Rate Problem Example
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Solving Complex Systems
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Plane Example Rate

• With a tailwind, an airplane makes a 900-mile
  trip in 2.25 hours. On the return trip, the plane
  flies against the wind (headwind) and makes the
  trip in 3 hours. What is the planes speed? What
  is the winds speed?

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Practice

• Hint remember that Ben paddles 3 mph in still
  water.

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More Practice

• Hint Notice the units are in minutes and yards,
  so solve the problem using those units.
• OR Usually we need hours and miles. Therefore, we
  could convert the units.

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Review

1. How do you set up a word problem?
2. How do you know if you set it up right?
3. How can you solve the system word problems?
4. What does the answer tell you about the system?