6 4 Applying Systems DAY 2 Rate Problems

6. 4 Applying Systems DAY 2: Rate Problems Essential Question: How do you write and solve rate problems?

Solving System Word Problems • Systems can be used to solve complex word problems that involve two or more variables. • To solve a word problem: 1) 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)

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.

Rate Problem Example

Solving Complex Systems

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 plane’s speed? What is the wind’s speed?

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

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.

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.