In January 2008, the temperature in parts of Minnesota fell from $41^{\circ} F$ to $-13^{\circ} F$ over a 24-hour period. What was the average temperature change per hour?
Answer (2)
Calculate the total temperature change: T o t a lC han g e = − 13 − 41 = − 5 4 ∘ F .
Calculate the average temperature change per hour: A v er a g e C han g e = 24 − 54 = − 2.2 5 ∘ F .
The average temperature change per hour is − 2.2 5 ∘ F .
The final answer is − 2.2 5 ∘ F .
Explanation
Understanding the Problem We are given that the temperature in Minnesota fell from 4 1 ∘ F to − 1 3 ∘ F over a 24-hour period. We want to find the average temperature change per hour.
Calculating Total Temperature Change First, we need to calculate the total temperature change. This is the final temperature minus the initial temperature: T o t a lC han g e = F ina lT e m p er a t u re − I ni t ia lT e m p er a t u re T o t a lC han g e = − 1 3 ∘ F − 4 1 ∘ F = − 5 4 ∘ F So the total temperature change is − 5 4 ∘ F .
Calculating Average Temperature Change Next, we need to calculate the average temperature change per hour. This is the total temperature change divided by the number of hours: A v er a g e C han g e = T im e P er i o d T o t a lC han g e A v er a g e C han g e = 24 h o u rs − 5 4 ∘ F = − 2.2 5 ∘ F / h o u r So the average temperature change per hour is − 2.2 5 ∘ F .
Examples
Understanding temperature changes is crucial in many real-world applications. For example, meteorologists use temperature data to predict weather patterns. In agriculture, knowing the rate of temperature change can help farmers protect crops from frost damage. Similarly, in construction, temperature variations affect the curing process of concrete and the structural integrity of buildings. By calculating average temperature changes, we can make informed decisions and prepare for potential environmental impacts.
The average temperature change per hour in Minnesota from January 2008 was calculated to be -2.25°F. This was determined by finding the total temperature change of -54°F over 24 hours and dividing by the number of hours. Therefore, the average decline in temperature was -2.25°F per hour.
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