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March 1st, 2016, 07:32 PM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  temperature problem
Temperatures can vary widely in the American Midwest in spring. One day in Indianapolis, the temperature changes from 41 degrees Fahrenheit to 82 degrees Fahrenheit in 6 hours. Jeffrey said, "That means it's now twice as warm as it was this morning!" Is he correct? Explain. Would Jeffrey be able to say the same thing if the temperature were converted to Celsius? Explain.

March 1st, 2016, 07:37 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Have you made any progress on the problem? Usually you post your working.

March 1st, 2016, 08:11 PM  #3 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  
March 1st, 2016, 08:35 PM  #4 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230 
Sure 82℉ is twice as far away from the arbitrary point 41℉, but what does that actually mean? Using absolute zero (total absence of energy in form of heat), your numbers actually mean something and doubling any temperature in Kelvin will be twice as warm. You can't say the same for any other (relative) scale like ℃ or ℉. Just as October 10th is not more "octobery" than October 5th. 
March 2nd, 2016, 01:42 AM  #5 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Azzajazz & Prakhar I actually don't know where to begin answering this question. Well, to draw an analogy... If a given line AB is 4 cm and another line CD is 8 cm, it is valid to say that CD is twice as long as AB. Then I think Jeffrey is right in claiming it has become twice as warm. Am I correct? 
March 2nd, 2016, 02:59 AM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,834 Thanks: 650 Math Focus: Yet to find out. 
Nice analogy! And it makes sense for the first part of the question. Have you tried converting the given temperatures to Celsius yet? 
March 2nd, 2016, 04:43 AM  #7  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
 
March 2nd, 2016, 06:41 AM  #8  
Newbie Joined: Mar 2016 From: UK Posts: 23 Thanks: 1  Quote:
The centigrade scale measures from 0  100 (freezing  boiling point of water). The Celsius scale, is essentially the same as Centigrade, albeit can go below 0 and above 100. Fahrenheit, the freezing point of water is 32 and boiling point is 212. This wiki article is quite good and shows the different conversions: https://en.wikipedia.org/wiki/Fahrenheit  
March 9th, 2016, 07:17 PM  #9 
Newbie Joined: Mar 2016 From: Philippines Posts: 2 Thanks: 0 
i still find it hard to understand temperature problem that's why i cannot answer it sometimes.


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temperatures can vary widely in the American Midwest in the spring. One day in Indianapolis the temperature changes from 41 degrees fahrenheit to 82 degrees fahrenheit in 6 hours. does that mean it is twice as warm?,applied advanced math
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