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On a winter evening at sundown, a Kansas City news station reports that the temperature is 2F-2 \, ^{\circ}\mathrm{F} and will drop by 2F2 \, ^{\circ}\mathrm{F} per hour until sunrise. At the same time, a Chicago news station reports that the temperature is 6F6 \, ^{\circ}\mathrm{F} and will drop by 4F4 \, ^{\circ}\mathrm{F} per hour.\newlineWhich equation can you use to find hh, the number of hours it will take the cities to reach the same temperature?\newlineChoices:\newline(A) 22h=64h-2 - 2h = 6 - 4h\newline(B) 2h2=6h42h - 2 = 6h - 4\newlineHow long will it take for the cities to reach the same temperature?\newlineSimplify any fractions.\newline____\_\_\_\_ hours\newline

Full solution

Q. On a winter evening at sundown, a Kansas City news station reports that the temperature is 2F-2 \, ^{\circ}\mathrm{F} and will drop by 2F2 \, ^{\circ}\mathrm{F} per hour until sunrise. At the same time, a Chicago news station reports that the temperature is 6F6 \, ^{\circ}\mathrm{F} and will drop by 4F4 \, ^{\circ}\mathrm{F} per hour.\newlineWhich equation can you use to find hh, the number of hours it will take the cities to reach the same temperature?\newlineChoices:\newline(A) 22h=64h-2 - 2h = 6 - 4h\newline(B) 2h2=6h42h - 2 = 6h - 4\newlineHow long will it take for the cities to reach the same temperature?\newlineSimplify any fractions.\newline____\_\_\_\_ hours\newline
  1. Set up Kansas City equation: Let's set up the equation for Kansas City first. The temperature starts at 2°F-2 \degree F and drops by 2°F2 \degree F each hour. So, after hh hours, the temperature in Kansas City will be 22h-2 - 2h.
  2. Set up Chicago equation: Now let's set up the equation for Chicago. The temperature starts at 6°F6 \degree F and drops by 4°F4 \degree F each hour. So, after hh hours, the temperature in Chicago will be 64h6 - 4h.
  3. Set temperatures equal: To find when the temperatures will be the same, we set the two expressions equal to each other. This gives us the equation 22h=64h-2 - 2h = 6 - 4h.
  4. Add 4h4h to both sides: Now we need to solve for hh. First, let's add 4h4h to both sides to get the hh terms on one side.\newline22h+4h=64h+4h-2 - 2h + 4h = 6 - 4h + 4h\newlineThis simplifies to 2+2h=6-2 + 2h = 6.
  5. Isolate term with hh: Next, we add 22 to both sides to isolate the term with hh.\newline2+2+2h=6+2-2 + 2 + 2h = 6 + 2\newlineThis simplifies to 2h=82h = 8.
  6. Solve for h: Finally, we divide both sides by 22 to solve for hh. \newline2h2=82\frac{2h}{2} = \frac{8}{2}\newlineThis gives us h=4h = 4.

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