jmc

Listing her first 5 times in ascending order, we get $$86,88,94,96,97$$ Because the final median is 92 and that is between 88 and 94, the final time must also lie in this spot. Thus, we have $$86,88,x,94,96,97$$ Because there are an even number of elements, the median is the mean of the center two. Thus, for the mean to be 92, $x$ must be $\boxed{90}\text{seconds}$.