Math Problem Statement

Lee is a meteorologist at a local weather station. He is studying a cold front that came in this morning. The temperature has dropped 6 degrees each hour for the last 7 hours. What was the change in temperature from the cold front after the 7 hours? Choose the sign of your answer to represent an increase or a decrease.

Solution

To solve this problem:

The temperature has dropped 66 degrees per hour for 77 hours.

The total change in temperature is calculated as: Total change=Rate of change per hour×Number of hours\text{Total change} = \text{Rate of change per hour} \times \text{Number of hours}

Substitute the values: Total change=6(degrees/hour)×7(hours)\text{Total change} = -6 \, (\text{degrees/hour}) \times 7 \, (\text{hours}) Total change=42degrees\text{Total change} = -42 \, \text{degrees}

The negative sign represents a decrease in temperature.

Final Answer: The temperature change was 42-42 degrees.


Would you like further details or clarifications? Here are 5 related questions to extend your understanding:

  1. If the temperature had increased 5 degrees per hour for 4 hours, what would the total change in temperature be?
  2. What would the new temperature be if the starting temperature was 20 degrees before the 7-hour drop?
  3. How would you represent this problem on a graph of temperature versus time?
  4. If the rate of temperature drop was halved, how would the total change differ after 7 hours?
  5. How can you represent positive and negative changes mathematically in other real-world situations?

Tip: Always associate the sign of a number with its meaning (e.g., negative for decrease, positive for increase) to keep track of changes effectively!

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Math Problem Analysis

Mathematical Concepts

Multiplication
Negative Numbers
Rate of Change

Formulas

Total change = Rate of change per hour × Number of hours

Theorems

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Suitable Grade Level

Grade 6-8