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?
If it was T, then
T-18-8+1+2+4+5 = 34
T = 48
To find the temperature at 6 am on the first day, we'll need to go step by step and track the changes in temperature.
1. The temperature dropped 18 degrees F between 6 am and 6 pm. So, at 6 pm, the temperature was x - 18 degrees F, where x is the temperature at 6 am.
2. During the night, the temperature fell another 8 degrees F. So, at the start of the night, the temperature was (x - 18) - 8 degrees F.
3. The next information we have is about the temperature at 6 am, where it started rising. The first hour it rose 1 degree F, so the temperature at 7 am is ((x - 18) - 8) + 1 = x - 25 degrees F.
4. The second hour it rose 2 degrees F, so the temperature at 8 am is (x - 25) + 2 = x - 23 degrees F.
5. The third hour it rose 4 degrees F, so the temperature at 9 am is (x - 23) + 4 = x - 19 degrees F.
6. The temperature rose another 5 degrees F during the day. So at 4 pm, the temperature was (x - 19) + 5 = x - 14 degrees F.
7. Finally, we are given that at 4 pm, the temperature was 31 degrees F. So, x - 14 = 31.
We can solve this equation to find the value of x, which is the temperature at 6 am on the first day.
x - 14 = 31
x = 31 + 14
x = 45
Therefore, the temperature at 6 am on the first day was 45 degrees F.
To find the initial temperature at 6 am on the first day, we need to work backwards and subtract the changes in temperature.
Let's calculate step-by-step:
1. The temperature dropped 18 degrees between 6 am and 6 pm, so at 6 pm it was 31°F - 18°F = 13°F.
2. During the night, the temperature fell another 8 degrees, so the temperature at 6 am the next morning was 13°F - 8°F = 5°F.
3. The temperature then started rising. It rose 1 degree in the first hour, 2 degrees in the second hour, and 4 degrees in the third hour, totaling 1°F + 2°F + 4°F = 7°F.
4. Adding the 7-degree increase to the temperature at 6 am gives us 5°F + 7°F = 12°F.
5. Lastly, the temperature rose another 5 degrees during the day, so the temperature at 4 pm was 12°F + 5°F = 17°F.
Therefore, the temperature at 6 am on the first day was 17°F.