6 5 Applying Systems DAY 2 Rate Problems

6. 5 Applying Systems DAY 2: Rate Problems Algebra 9. 0, 15. 0

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.

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?