Final answer:
It will take approximately 9 hours and 43 minutes for the temperature in Frostport to reach -20F from its current temperature of 8F, dropping at a rate of 3.5 degrees per hour.
Step-by-step explanation:
In order to determine the number of hours until the temperature reaches -20F, we first need to calculate the difference between the starting temperature of 8F and the desired temperature of -20F. This difference is 28F. Since the temperature is dropping at a rate of 3.5 degrees per hour, we can divide the difference by the rate to find the number of hours it will take. 28F / 3.5 degrees per hour = 8 hours. However, this only accounts for the temperature dropping from 8F to 0F. We still need to account for the remaining 20 degrees to reach -20F. This will take an additional 20/3.5 = 5.71 hours, or approximately 5 hours and 43 minutes. Adding these two times together gives us a total of 8 hours + 5 hours and 43 minutes = 9 hours and 43 minutes.
We can also use the formula t = (x-x0)/a, where t is time in hours, x is the final temperature, x0 is the initial temperature, and a is the rate of change. Plugging in the values for our problem, we get t = (-20 - 8) / (-3.5) = -28 / (-3.5) = 8 hours. This only gives us the time it takes for the temperature to drop from 8F to 0F. To find the total time, we need to add the time it takes for the temperature to drop from 0F to -20F, which can be found by substituting x = -20 and x0 = 0 into the formula, giving us t = (-20 - 0) / (-3.5) = -20 / (-3.5) = 5.71 hours. Again, adding these two times gives us a total of 9 hours and 43 minutes.
In conclusion, it will take approximately 9 hours and 43 minutes for the temperature in Frostport to reach -20F from its current temperature of 8F, dropping at a rate of 3.5 degrees per hour. This calculation accounts for both the initial drop from 8F to 0F and the remaining drop from 0F to -20F. By using the formula t = (x-x0)/a or by dividing the difference by the rate, we can accurately determine the time it will take for the temperature to reach the desired value.