Math Problem Statement

One spring day, Savannah noted the time of day and the temperature, in degrees Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 60°F. For the next 5 hours, the temperature rose 1°F per hour. For the next 2 hours, it rose 4°F per hour. The temperature then stayed steady until 6 p.m. For the next 6 hours, the temperature dropped 1°F per hour. The temperature then dropped steadily until the temperature was 69°F at midnight. Graph Savannah's data.

Solution

Let's break down the problem described in the image:

  • At 6 a.m., the temperature was 60°F.
  • For the next 5 hours, the temperature increased by 1°F per hour. So by 11 a.m., the temperature would be: 60+5=65F60 + 5 = 65^\circ \text{F}
  • For the following 2 hours, the temperature rose 4°F per hour. So by 1 p.m., the temperature would be: 65+(4×2)=73F65 + (4 \times 2) = 73^\circ \text{F}
  • The temperature remained steady at 73°F until 6 p.m..
  • After 6 p.m., the temperature started dropping by 1°F per hour for the next 6 hours, reaching midnight. Therefore, by midnight, the temperature would be: 736=67F73 - 6 = 67^\circ \text{F}

This temperature data can be plotted against the time of day, using 6 a.m. as the starting point and midnight as the ending point.

Step-by-step:

  1. 6 a.m.: Starting at 60°F.
  2. 6 a.m. to 11 a.m.: Temperature increases by 1°F each hour, reaching 65°F at 11 a.m.
  3. 11 a.m. to 1 p.m.: Temperature increases by 4°F each hour, reaching 73°F at 1 p.m.
  4. 1 p.m. to 6 p.m.: Temperature stays constant at 73°F.
  5. 6 p.m. to midnight: Temperature drops by 1°F each hour, reaching 67°F at midnight.

Would you like me to help you plot this graph step-by-step, or is there something specific you'd like assistance with?

Here are 5 relative questions:

  1. What would the temperature be at 3 p.m. given the data?
  2. How much total did the temperature increase between 6 a.m. and 1 p.m.?
  3. At what time did the temperature stop rising?
  4. How many hours did the temperature remain constant throughout the day?
  5. How would the temperature graph differ if the cooling period began at 4 p.m. instead of 6 p.m.?

Tip: When plotting graphs, always label the axes carefully and mark the points where changes in the rate of increase or decrease occur.

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Math Problem Analysis

Mathematical Concepts

Linear functions
Rate of change
Graphing

Formulas

y = mx + b (linear equation)
Slope = (change in temperature) / (change in time)

Theorems

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Suitable Grade Level

Grades 6-8