Question

m.14 solve equations with variables on both sides: word probl...
on a winter evening at sundown, a kansas city news station reports that the temperature is -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?
2h - 2 = 6h - 4
-2 - 2h = 6 - 4h
how long will it take for the cities to reach the same temperature?
simplify any fractions.
____ hours

Explanation:

Part 1: Choosing the Correct Equation

Step 1: Analyze Kansas City's Temperature

Kansas City starts at \(-2^\circ F\) and drops \(2^\circ F\) per hour. So after \(h\) hours, its temperature is \(-2 - 2h\).

Step 2: Analyze Chicago's Temperature

Chicago starts at \(6^\circ F\) and drops \(4^\circ F\) per hour. So after \(h\) hours, its temperature is \(6 - 4h\).

Step 3: Set Temperatures Equal

To find when they are equal, set \(-2 - 2h = 6 - 4h\).

Step 1: Add \(4h\) to Both Sides

To get all \(h\) terms on one side, add \(4h\) to both sides: \(-2 - 2h + 4h = 6 - 4h + 4h\), which simplifies to \(-2 + 2h = 6\).

Step 2: Add 2 to Both Sides

Add 2 to both sides: \(-2 + 2h + 2 = 6 + 2\), so \(2h = 8\).

Step 3: Divide by 2

Divide both sides by 2: \(\frac{2h}{2} = \frac{8}{2}\), so \(h = 4\).

Answer:

\(-2 - 2h = 6 - 4h\)

Part 2: Solving for \(h\)