They did the same thing in Amsterdam. There were a lot complaints at the beginning, but the city became much nicer in the end. Immediate improvement was the reduction of noise. Studies have shown that there was only a 5% increase of travel time. For example, that would be 1 minute on a 20 minute trip. That is because the largest determinant of average speed are the intersections and not the maximum speed limit.
Even cycling into the city from my neighbouring town (~10 km) can be faster than a car at peak rush hour, because city traffic is just an absolute gridlock (this is in Galway Ireland, the traffic of which is notoriously bad even by Irish standards, but still).