On a winter evening at sundown, a Kansas City news station reports that the temperature is

Question

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2°F and will drop by 2°F per hour until sunrise. At the same time, a Chicago news station reports that the temperature is 6°F and will drop by 4°F per hour.
Which equation can you use to find h, the number of hours it will take the cities to reach the same temperature?
How long will it take for the cities to reach the same temperature?
Simplify any fractions.

Answer 1

To find out when the temperatures in Kansas City and Chicago will be the same, we can set up an equation based on the given information about how the temperatures will change over time.

1. Kansas City:

   • Initial temperature: -2°F
   • Rate of temperature drop: 2°F per hour
   • Temperature after \( h \) hours: \[ T_{KC} = -2 - 2h \]

2. Chicago:

   • Initial temperature: 6°F
   • Rate of temperature drop: 4°F per hour
   • Temperature after \( h \) hours: \[ T_{Chi} = 6 - 4h \]

Now, we want to find \( h \) when the temperatures are equal: \[ -2 - 2h = 6 - 4h \]

Next, let’s solve the equation for \( h \).

3. Rearranging the equation:

   • Add \( 4h \) to both sides: \[ -2 - 2h + 4h = 6 \] \[ -2 + 2h = 6 \]

   • Add 2 to both sides: \[ 2h = 6 + 2 \] \[ 2h = 8 \]

   • Divide by 2: \[ h = \frac{8}{2} = 4 \]

Thus, it will take 4 hours for the temperatures in Kansas City and Chicago to reach the same temperature.

Final Results:

• The equation to use is: \[ -2 - 2h = 6 - 4h \]
• The time it will take for the cities to reach the same temperature is: \[ h = 4 \text{ hours} \]