the temperature dropped 18 degrees F between 6 am and 6 pm. during the night the temperature fell another 8 degree F. at 6 am the temperature started rising. It rose 1degree F the first hour, 2 degree F the second hour, and 4 degree the third hour. The temperature rose another 5 degree F during the day. At 4pm the tempersture climbed to 31degree F. What was the temperature at 6 am the first day?
To find the temperature at 6 am on the first day, we need to track the temperature changes throughout the day. Let's break down the given information step by step.
1. The temperature dropped 18 degrees Fahrenheit between 6 am and 6 pm.
So, the temperature at 6 pm would be the initial temperature minus 18 degrees, denoted as T1 - 18.
2. During the night, the temperature fell another 8 degrees Fahrenheit.
So, the temperature at 6 am the next day would be 6 pm temperature minus 8 degrees, denoted as (T1 - 18) - 8.
3. The temperature started rising at 6 am and increased 1 degree Fahrenheit the first hour, 2 degrees the second hour, and 4 degrees the third hour.
To calculate the temperature after three hours of rising, we add the elevations: (T1 - 18) - 8 + 1 + 2 + 4.
4. The temperature continued to rise, adding another 5 degrees Fahrenheit during the day.
To calculate the temperature at 4 pm, we add the additional 5 degrees to our previous result: [(T1 - 18) - 8 + 1 + 2 + 4] + 5.
5. Finally, at 4 pm, the temperature reached 31 degrees Fahrenheit.
So, we can set up an equation: [(T1 - 18) - 8 + 1 + 2 + 4] + 5 = 31.
Simplifying the equation:
(T1 - 18) - 8 + 1 + 2 + 4 + 5 = 31,
T1 - 18 - 8 + 1 + 2 + 4 + 5 = 31,
T1 - 14 = 31.
To isolate T1 (the temperature at 6 am on the first day), we add 14 to both sides:
T1 - 14 + 14 = 31 + 14,
T1 = 45.
Therefore, the temperature at 6 am on the first day was 45 degrees Fahrenheit.