$4\mathrm{.}7$ A computer has a cache, main memory, and a disk used for virtual memory. If a referenced word is in the cache, $9ns$ are required to access it$.$ If it is in main memory but not in the cache, $80ns$ are needed to load it into the cache, and then the reference is started again. If the word is not in main memory, $8ms$ are required to fetch the word from disk, followed by $80ns$ to copy it to the cache, and then the reference is started again. The cache miss rate is $9\%$ and the main memory miss rate is $30\%.$ What is the average time in nanoseconds required to access a referenced word on this system?