Math Problem Statement

Tyler says the temperature dropped faster between 4 p.m. and 6 p.m. Mai says the temperature dropped faster between 6 p.m. and 10 p.m. Who do you agree with? Explain your reasoning/show your work.

Solution

In the image, the recorded temperatures at different times are as follows:

  • 4 p.m.: 25°C
  • 6 p.m.: 17°C
  • 10 p.m.: 8°C

The question is about the rate at which the temperature dropped between these times. Tyler says the temperature dropped faster between 4 p.m. and 6 p.m., while Mai says it dropped faster between 6 p.m. and 10 p.m.

Let’s calculate the rate of temperature change for both time periods.

  1. From 4 p.m. to 6 p.m.:
    Temperature change = 25°C - 17°C = 8°C
    Time interval = 6 p.m. - 4 p.m. = 2 hours
    Rate of change = 8°C ÷ 2 hours = 4°C per hour.

  2. From 6 p.m. to 10 p.m.:
    Temperature change = 17°C - 8°C = 9°C
    Time interval = 10 p.m. - 6 p.m. = 4 hours
    Rate of change = 9°C ÷ 4 hours = 2.25°C per hour.

Conclusion:
The temperature dropped faster between 4 p.m. and 6 p.m. at a rate of 4°C per hour, compared to the rate of 2.25°C per hour between 6 p.m. and 10 p.m. Thus, I agree with Tyler's statement that the temperature dropped faster between 4 p.m. and 6 p.m.

Would you like further details or explanations? Let me know!

Here are some related questions for you:

  1. How would the rate of temperature change be affected if the time intervals were different?
  2. What other factors might affect the rate of temperature change over time?
  3. How would you calculate the average rate of temperature change over the entire evening (from 4 p.m. to 10 p.m.)?
  4. If the temperature had dropped 5°C between 4 p.m. and 6 p.m., how would that change the answer?
  5. Can the rate of temperature change be constant during the evening?

Tip: Always remember to check the units of time and temperature when calculating rates to ensure consistency!

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Math Problem Analysis

Mathematical Concepts

Rate of change
Time intervals
Temperature change

Formulas

Rate of change = (Final value - Initial value) / Time interval

Theorems

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Suitable Grade Level

Grades 5-7