In a virtual memory system, it takes $10$ ns to access a word in the cache. If a word is in main memory but mot in the cache. $30$ ns are needed to load it into the cache, and then the reference to it is started again. If the word is not in main memory, $12$ms are required to fetch the word from disc, followed by $30$ ns to copy it to the cache, and then the reference is started again.

Let the cache hit ratio be $0\mathrm{.}9$ and the main$-$memory hit ratio be $0\mathrm{.}6.$ What is the average time to access a reference word in the system?