Correlation between time to event data and continuous data
There is nothing wrong with using Pearson's correlation coefficient (frequently called THE correlation coefficient) with these variables. I would also have a look at Spearman's rank correlation coefficient. It is less sensitive to extreme values. 

http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient

However, both coefficients have the drawback that they only measure linear relationships. Hence it is worthwile to have a look at the scatterplot of the variables. Adding a smoother to the graph can be worthwile too, especially  if the plot is clutterd and you have trouble to spot a relationship with the naked eye.