One morning in Austin, Texas, the temperature was 80 °F and rose by 2 °F per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was 72 °F and rose by 4 °F per hour. Which equation can you use to find h, the number of hours it took for the cities to reach the same temperature? Choices: (A)80 + 2h = 72 + 4h (B)80h + 2 = 72h + 4 How long did it take for the cities to reach the same temperature? Simplify any fractions. ____ hours

Question

One morning in Austin, Texas, the temperature was 80 °F and rose by 2 °F per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was 72 °F and rose by 4 °F per hour. Which equation can you use to find h, the number of hours it took for the cities to reach the same temperature?   Choices: (A)80 + 2h = 72 + 4h (B)80h + 2 = 72h + 4  How long did it take for the cities to reach the same temperature? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Equations Equal: To find the equation that represents the time it takes for both cities to reach the same temperature, we need to set the temperature increase expressions for both cities equal to each other. This is because we are looking for the point in time when the temperatures are the same.Austin's Temperature Expression: For Austin, Texas, the temperature started at 80 °F and increased by 2 °F per hour. So, the temperature in Austin after h hours can be represented by the expression 80 + 2h.Little Rock's Temperature Expression: For Little Rock, Arkansas, the temperature started at 72 °F and increased by 4 °F per hour. So, the temperature in Little Rock after h hours can be represented by the expression 72 + 4h.Solve for h: To find when the temperatures are the same, we set the expressions equal to each other: 80 + 2h = 72 + 4h. This is the correct equation to use, which corresponds to choice (A).Subtract 2h: Now we solve for h. First, we subtract 2h from both sides to get the h terms on one side: 80 = 72 + 2h.Isolate Term with h: Next, we subtract 72 from both sides to isolate the term with h: 80 - 72 = 2h.Simplify Left Side: Now we simplify the left side: 8 = 2h.Divide Both Sides: Finally, we divide both sides by 2 to solve for h: 8/2 = h.Final Answer: Simplifying the right side gives us h = 4. So, it took 4 hours for the cities to reach the same temperature.

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