When using the Fourier font for text is it possible to use the standard times new roman latex font (or any other) for equations?
The standard font defined by LaTeX is not Times; but neither Computer Modern nor Times mix with Utopia. The Fourier package uses a math font specially tailored for combining with the main typeface that's Utopia.
While it is possible to use a different math font than Fourier when the text font is Utopia, it's really not recommendable, so the answer to your question is “yes, it's possible, but, please, don't do it”. Let's see some examples why one shouldn't do it.
1. Utopia for text and Computer Modern for math
This is completely unacceptable
2. Utopia for text and Times for math
The differences between text and math are not as big as in the previous experiment, but still evident: the x-height and thickness of the fonts are too far apart, making also this combination unacceptable.
3. Utopia for text and Fourier for math
This is the only acceptable solution if you want Utopia for text. Just