6.4 Applying Systems DAY 2: Rate Problems

1
6.4 Applying SystemsDAY 2 Rate Problems

• Essential Question
• How do you write and solve rate problems?

2
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)

3
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.

4
Rate Problem Example
5
Solving Complex Systems
6
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?

7
Practice

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

8
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.

9
Summary

• Answer the essential question in detailed,
  complete sentences.
• How do you write and solve rate problems?
• Write 2-4 study questions in the left column to
  correspond to the notes.