Systems of Equations

Systems of Equations

Distance/ Rate/ Time Questions

Distance/ Rate/ Time

Starting with "distance word problems"

What does this mean?

• Distance Word Problems are also called "uniform rate". It means they change at the same rate.

• If you think about these problems algebraically they are not to tricky, but you need to learn to set them up.

• The tricky part is you need to make sure they are talking the same units. Miles per hour should be compared to miles per hour, not miles per minute.

Traveling Boss Example

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

Poll

Do you feel you could set up an algebra equation for that problem right now?

• Yes

• No

Breaking down the Problem

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

• First, you should look at what the question is asking. In this problem, it is asking for two answers. How fast the plane flew for the first part of the trip and how much it flew for the remainder of the trip.

Multiple Select

A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

Looking at the equation which numbers will I use? (Check all needed)

• Distance

• Speed

• Time

• Tailwind

Notes 1

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

• I like to use tables so let's put a table together. (Write this on your paper)

Notes 1

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

• Let's fill in the information we know.

Notes 1

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

• Lets use some algebra to think about how to fill in the other boxes.

Multiple Select

On your notes do you have written... (Remember you are going to text Clark your notes at the end of this lesson)

• First Part, Second Part, Total

• Distance including; d, 555-d, 555

• Speed including; 105, 115

• Time including; t, 5-t, 5

Problem 1

• A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

• After setting up the table it will be easy.

Multiple Select

That still does not give us the entire answer to the original question. The question asked, "For how long did the plane fly at each speed?"

You need to go back to the question and substitute in 2 for t. Look at the choices below click the ones that are correct.

• The first part of the flight took 2 hours.

• The first part of the flight took 3 hours.

• The second part of the flight took 2 hours.

• The second part of the flight took 3 hours.