The total number miles driven on roads will almost always go up when you build more roads, just like increasing the supply of apples will lead to more apples being eaten. (The rare exceptions would be if there are a fixed number of people taking a long circuitous route from A to B, and a shortcut road is built; then the fixed number of drivers would get there more directly, reducing the total number of miles driven.) What normally happens with apples is that the price of apples goes down when there is new supply, roughly analogous to a decrease in congestion (i.e., the "price", in their time, that drivers pay to use a road).

When people talk about induced demand as an argument for building roads, they are claiming that induced demand will mean that congestion on the existing roads will increase (or at least not decrease). Here you have to take into account that most places where you build roads are growing for exogenous reason, so it doesn't make sense to compare post-construction congestion to pre-construction congestion. You have to compare post-construction congestion to the counterfactual where no construction was done. When you do that, you find (my emphasis)

> for every 100 percent increase in capacity there’d be an eighty percent increase in travel, reflecting increased travel speeds and land use shifts along improved corridors. However, only around half the increases in speed and growth in building permits was due to the added capacity. Factors like employment and income growth accounted for the other half. Accordingly, the traffic gains that one can attribute to the added capacity is actually around half of eighty percent, or forty percent. This is substantially less than reported by past induced-demand studies.

http://www.uctc.net/access/22/Access%2022%20-%2004%20-%20Ind...

The answer to all of this is well known: dynamically price road usage to keep roads at max capacity without noticeable congestion. Then each new road built is pure benefit.