In my home city of 's-Hertogenbosch, a canal is being moved. It used to run through the city center, causing a lot of open bridges holding up bicycles, cars and buses alike. In the new situation, it will run to the east of the city, between 's-Hertogenbosch and Rosmalen (a former municipality that was joined with 's-Hertogenbosch about 15 years ago). Of course, a number of new bridges have to be built to cross the new canal.
One place that was much influenced by the new canal is Empel, a village to the northeast. It used to have three important routes out, to the west to 's-Hertogenbosch, to the south to Rosmalen and to the east to a major regional road. The latter two are cut by the canal, and have been replaced by a single road, which follows the south road for some distance, then turns east, crosses the canal and ends at that same regional road, halfway between the end of the other two roads.
Because the new road is to have more traffic than the old road, both the road and the cyclepath along it had to be widened for the part that remains. For this, it had to be closed. The municipality decided to rent a piece of land beside it to build a temporary cyclepath. Car drivers had to take a more roundabout route (using the east exit and the regional road), but cyclists could keep using the old road until the new one was finished.
It may seem remarkable that such a provision was given to cyclists but not to car drivers. But I do think there are logical reasons for it. One is undoubtedly that constructing a temporary cyclepath is much cheaper, both in money and in land use, than a temporary road. But another is the realization that different modes have different priorities. The alternative road that the car drivers had to take was longer, but it also had higher speed limits and even more so higher practical maximum speed. The roads were wider and had less curves. Thus, for car drivers the disadvantage was much smaller than the difference in length would suggest. For cyclists on the other hand, higher speeds and wider car lanes are no advantage whatsoever (they would even be a disadvantage if it wasn't for the segregated cycling infrastructure provided). For them, the difference in length would thus work much more negative than for car drivers.
A similar case I met in Lunteren, a town that I sometimes visit during my Summer holidays. Simplifying the situation for clarity, there used to be two main roads, one running north-south through town, the other going west from the town center, to a motorway running north-south some distance away. A bypass was constructed, allowing north-south traffic to go around on the west. The bypass is disallowed for cyclists, and some length of the original road in the center was closed off for cars, forming a pedestrian road with bicycles allowed. Both modes profit from this change: Car drivers have a route that is longer, but considerably faster, with higher maximum speed and much fewer crossings. Cyclists have kept the old, short route, but much more pleasant now that the number of cars is greatly reduced.