If the temperature continues to drop at the same rate, the temperature after 2 hours will be -2°F
After a small online search, I've found that the actual question says:
"In the afternoon the temperature was 52 °F. A strong arctic cold front caused the temperature to drop 38 degrees in 4 3/4 hours. If the temperature continues to drop at the same rate, what will the temperature be after 2 hours?"
The initial temperature is 52°F.
We know that for some reason, the temperature drops 38°F at a constant rate in (4 + 3/4) hours.
Then to find that constant rate, we need to find the quotient between the total temperature drop (-38°F) and the total time that it takes (4 + 3/4) hours.
First, let's rewrite the number as a single fraction:
4 + 3/4 = 16/4 + 3/4 = 19/4
then:
(4 + 3/4) hours = (19/4) hours.
Then the constant rate is:
r = (-38°F)/( (19/4) h) = (4/19)*(-38) °F/h
= -8 °F/h
This means that each hour that passes, the temperature decreases by 8°F
Then we can write the temperature as:
T(x) = 52°F - (8 °F/h)*x
where x is the time in hours.
The question says:
"If the temperature continues to drop at the same rate, what will the temperature be after 2 hours?"
Because of the word "continues", this refers to two hours after the (4 + 3/4) hours of the initial decrease temperature.
2 hours after that is:
(4 + 3/4) h + 2 h = (6 + 3/4) h
So we just need to evaluate the temperature equation in x = (6 + 3/4) hours.
T( 6 + 3/4 hours) = 52°F - (8 °F/h)*(6 + 3/4) h
= 52°F - 54°F = -2°F