Question: TV Frequencies - Question II

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Comment on TV Frequencies - Question II

Okenwa2018 - January 16, 2019
This question comes with a picture. Unfortunately i am unable to include the picture, however, i shall provide the relevant info depicted in the picture. In the picture, the highest temperature is 86 degrees Fahrenheit while the lowest is 74 degrees Fahrenheit. The question then asked: The euation C = (5/9)(F-32) represents the relationship between temperature C in degrees Celsius and the corresponding temperature F in degrees Fahrenheit. The graph shows the high temperature, in degrees Fahrenheit, on each day of a certain week. Which of the following is closest to the range of the high temperatures for the week, in degrees Celsius?

The correct answer is 7. And it seems that the best way to arrive at that answer is to first separately convert the highest and lowest temperatures in F to C (with the formula provided), and then subtract the now converted temperatures: the lowest figure, now in Celsius, from the highest figure, now in Celsius; which gives 7.

My question is, why is it incorrect to do the subtraction first (while still in degrees F) and after convert the outcome of the subtraction into C, which will give us 12?
greenlight-admin's picture

greenlight-admin - January 16, 2019

Great question!!!

The main issue has to do with nature of the conversion formula C = (5/9)(F-32).

This formula is only useful for converting the ACTUAL temperature in one format to the other format. The formula does not help use convert temperature DIFFERENCES.

For example, if we're familiar with the Fahrenheit scale, we know that there's a BIG difference between a temperature of 98° F and a temperature of 66° F. In fact, we're talking about a 32° F DIFFERENCE.

Now see what happens if we try to convert this temperature DIFFERENCE (of 32° F) to its Celsius equivalent.

We get: C = (5/9)(32 - 32)
= (5/9)(0)
= 0

So 32° Fahrenheit = 0° Celsius

0° Celsius suggests that the is NO temperature difference between the two temperatures (98° F and 66° F). This, of course, is not true.

So, if we want the temperature difference in CELSIUS, we first need to know each temperature in CELSIUS.

Does that help?

Cheers,
Brent

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