A computer has a cache, main memory, and a disk used for virtual memory. If a referenced word is in the cache, $20$ ns are required to access it$.$ If it is in main memory but not in the cache, $60$ ns are needed to load it into the cache, and then the reference is started again. If the word is not in main memory, $12$ ns are required to fetch the word from the disk, followed by $60$ ns to copy it to the cache, and then the reference is started again. The cache hit ratio is $0\mathrm{.}9$ and the main memory hit ratio is $0\mathrm{.}6.$ What is the average time in nanoseconds required to access a referenced word on this system?