One afternoon, a news station in San Pablo reports that the temperature is 90 °F and will drop by 2 °F per hour. At the same time, a news station in Santa Rosa reports that the temperature is 97 °F and will drop by 4 °F per hour. Which equation can you use to find h, the number of hours it will take for the cities to reach the same temperature? Choices: (A)90 - 2h = 97 - 4h (B)90 + 2h = 97 - 4h How long will it take for the cities to reach the same temperature? Simplify any fractions. ____ hours

Question

One afternoon, a news station in San Pablo reports that the temperature is 90 °F and will drop by 2 °F per hour. At the same time, a news station in Santa Rosa reports that the temperature is 97 °F and will drop by 4 °F per hour. Which equation can you use to find h, the number of hours it will take for the cities to reach the same temperature?   Choices: (A)90 - 2h = 97 - 4h (B)90 + 2h = 97 - 4h  How long will it take for the cities to reach the same temperature? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Up Equation: To find when the temperatures in San Pablo and Santa Rosa will be the same, we need to set up an equation where the temperatures as functions of time (h) are equal. Since the temperature in San Pablo starts at 90 °F and decreases by 2 °F per hour, its temperature after h hours is 90 - 2h. Similarly, the temperature in Santa Rosa starts at 97 °F and decreases by 4 °F per hour, so its temperature after h hours is 97 - 4h. To find when the temperatures are the same, we set these two expressions equal to each other.Use Correct Equation: The correct equation to use is (A) 90 - 2h = 97 - 4h, because it represents the temperatures in both cities decreasing over time and being set equal to each other to find the point in time when they are the same.Solve for h: Now we solve the equation 90 - 2h = 97 - 4h for h. First, we can add 4h to both sides to get all the h terms on one side of the equation. 90 - 2h + 4h = 97 - 4h + 4h This simplifies to: 90 + 2h = 97Isolate Term: Next, we subtract 90 from both sides to isolate the term with h. 90 + 2h - 90 = 97 - 90 This simplifies to: 2h = 7Divide by 2: Finally, we divide both sides by 2 to solve for h. 2h / 2 = 7 / 2 This simplifies to: h = 7/2Convert to Decimal: Since 7/2 is a fraction, we can convert it to a mixed number or decimal to make it easier to understand. 7 divided by 2 is 3.5. So, h = 3.5

Full solution

More problems from Solve linear equations with variables on both sides: word problems

Related topics