Final answer:
To find when Houston's temperature will be at least the same as Amarillo's, set the starting temperatures and rates of increase into an inequality, 68 + 4t ≥ 74 + 2t. Solving for t, we find that t ≥ 3, indicating it will take at least 3 hours for the temperatures to be the same.
Step-by-step explanation:
To write an inequality representing when the temperature in Houston will be at least the same as in Amarillo, we must set up an equation that considers the initial temperatures and the rates at which they increase. Amarillo starts at 74°F and increases at a rate of 2°F per hour, which we can express as 74 + 2t, where t is the time in hours. Houston starts at 68°F and increases at a rate of 4°F per hour, represented by 68 + 4t. To find when the temperatures will be the same, we set up the inequality 68 + 4t ≥ 74 + 2t.
Solving for t, we subtract 2t from both sides to get 2t ≥ 6, and then divide both sides by 2 to isolate the variable t, yielding t ≥ 3. Therefore, it will take at least 3 hours for the temperature in Houston to be at least the same as Amarillo's temperature.