In the afternoon the temperature was 52 °F. A strong arctic cold front caused the temperature to drop 38 degrees in 434 hours. If the temperature continues to drop at the same rate, what will the temperature be after 2 hours? °F

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