Answer:
574.25 °
Step-by-step explanation:
To know this, we need to get the expressions to calculate °F and °K.
In the case of Kelvin:
°K = °C + 273
in fahrenheit:
°F = 9/5(°C + 32)
Now, in order to know the temperature which both Kelvin and Fahrenheit are the same, we need to use both above equations, and solve for °C.
°C = °K - 273 (1)
°C = 5/9(°F - 32) (2)
Using 1 and 2 into a same expression:
°K - 273 = 5/9(°F - 32)
With this, we need to know now the moment which K = F, so, all we need to do is replace the F for the K in the above expression. Doing this, we have:
°K - 273 = 5/9(°K - 32)
°K = 0.555(°K - 32) + 273
°K = 5/9K - 17.78 + 273
°K - 5/9K = 255.22
4/9°K = 255.22
°K = 255.22 * 9 / 4
°K = 574.25 °
And this is the temperature in which both Kelvin and Fahrenheit are the same.