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One afternoon, a news station in San Pablo reports that the temperature is 90F90 \, ^{\circ}\mathrm{F} and will drop by 2F2 \, ^{\circ}\mathrm{F} per hour. At the same time, a news station in Santa Rosa reports that the temperature is 97F97 \, ^{\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 for the cities to reach the same temperature?\newlineChoices:\newline(A) 90+2h=974h90 + 2h = 97 - 4h\newline(B) 902h=974h90 - 2h = 97 - 4h\newlineHow long will it take for the cities to reach the same temperature?\newlineSimplify any fractions.\newline____\_\_\_\_ hours\newline

Full solution

Q. One afternoon, a news station in San Pablo reports that the temperature is 90F90 \, ^{\circ}\mathrm{F} and will drop by 2F2 \, ^{\circ}\mathrm{F} per hour. At the same time, a news station in Santa Rosa reports that the temperature is 97F97 \, ^{\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 for the cities to reach the same temperature?\newlineChoices:\newline(A) 90+2h=974h90 + 2h = 97 - 4h\newline(B) 902h=974h90 - 2h = 97 - 4h\newlineHow long will it take for the cities to reach the same temperature?\newlineSimplify any fractions.\newline____\_\_\_\_ hours\newline
  1. Understand the problem: Understand the problem.\newlineWe need to find the time hh when the temperatures in San Pablo and Santa Rosa will be equal. San Pablo starts at 90°F90 \degree\text{F} and decreases by 2°F2 \degree\text{F} per hour, while Santa Rosa starts at 97°F97 \degree\text{F} and decreases by 4°F4 \degree\text{F} per hour.
  2. Set up the equation: Set up the equation.\newlineSince the temperatures are decreasing, we should subtract the hourly change from the initial temperatures. The correct equation is the one that represents this situation.
  3. Choose the correct equation: Choose the correct equation.\newlineThe correct equation is (B) 902h=974h90 - 2h = 97 - 4h, because it shows the temperatures decreasing from their initial values by their respective rates per hour.
  4. Solve the equation for h: Solve the equation for h.\newline902h=974h90 - 2h = 97 - 4h\newlineAdd 4h4h to both sides to get all hh terms on one side:\newline902h+4h=974h+4h90 - 2h + 4h = 97 - 4h + 4h\newline90+2h=9790 + 2h = 97\newlineSubtract 9090 from both sides to isolate the hh terms:\newline2h=97902h = 97 - 90\newline2h=72h = 7\newlineDivide both sides by 22 to solve for hh:\newline4h4h11\newline4h4h22

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