Question

One morning in Austin, Texas, the temperature was 80°F and rose by 2°F per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was 72°F and rose by 4°F per hour.

Which equation can you use to find h, the number of hours it took for the cities to reach the same temperature?
How long did it take for the cities to reach the same temperature? Simplify any fractions.
___ hours

Answer 1

It took 4 hours for the two cities to reach the same temp.

Explanation:

Part 1

First, you will write an expression for each city.

Austin starts at 80°F and rises 2°F per hour. 80 is our starting point. 2 is how much is added each hour. The per hour means we need a variable.

`80 +2h`

Little Rock starts at 72°F and rises 4° per hour. 72 is our starting point. 4 is how much is added per hour. The per hour means we need a variable.

`72+4h`

Second, you want to know when the cities are equal, so you set these expressions equal to each other.

`80+2h=72+4h`

Part 2

`80+2h=72+4h`

This is an equation with variables on both sides. You will need to follow a few steps to solve these problems.

`80+2h=72+4h`

Step 1: look for grouping symbols. This problem does not have any visible or invisible grouping symbols.

`80+2h=72+4h`

Step 2: Look at the left side. Are there any like terms? This problem does not have any like terms on the left side. Look at the right side. Are there any like terms? This problem does not have any like terms on the right side.

Step 3: Are there variables on the left and right side of the equal sign? (Look to the left of the equal sign; you will see 2h. The h is a variable on the left side. Look to the right of the equal sign; you will see 4h. The h is a variable on the right side.)

• The answer is yes. You will subtract the variable with the smaller coefficient from each side of the equal sign. (
  `2 < 4`)
  `80+2h-2h=72+4h-2h`
• 
  `80=72+2h`

Step 4: Are there constants on the left and right sides of the equal sign?

• The answer is yes (80 is on the left, and 72 is on the right.) You will subtract the constant on the same side on the equal sign as the variable. The 72 is on the right side with the 2h. You will subtract 72 from the left and right sides of the equal sign.
  `80-72=72-72+2h`
• 
  `8=2h`

Step 5: Does the variable have a coefficient other than 1? (Is there a number written with the variable? Is the variable not 1?)

• Yes, the coefficient is 2. You will divide the right and left sides by 2.
  `(8)/(2) =(2h)/(2)` (8 divided by 2 equals 2, 2h divided by 2 equals 1h)
• 
  `4=h`

You have now solved the equation for the variable. Remember h was defined in the problem as "the number of hours it took for the cities to reach the same temperature." This means that it took 4 hours for the cities to reach the same temperature. You can check this with a simple check

You substitute the 4 in the original expressions. If you did the work correctly, you will get the same answer for both equations.

`80+2(4)\\80+8\\88`

`72+4(4)\\72+16\\88`

Since both expressions produced the same answer when 4 was substituted the answer is correct.

Answer 2

80+2h=72+4h

4hours

Explanation:

80+2h=72+4h

80-72=4h-2h

8=2h

h=8/2

h=4