Motorist

Time on the expressway is $\dfrac{100 ~ \text{miles}}{ 80 ~ \text{mph}} = 1.25h$ $(1\text{h}:15\text{m})$

He spent another $45$ minutes on other roads, so his whole journey was $1\text{h}:15\text{m} ~ \text{plus} ~ 45\text{m} = 2 \text{hours}.$

If his average speed over the $2$ hours was $65 \text{mph},$ then he must have traveled $2\text{h}\times 65 \text{mph} = 130 ~ \text{miles}$

So he must have driven $130 - 100 = \boxed{30 ~ \text{miles}}$ on the other roads.