Regatta race schedule

At a certain regatta the number of races on each day varied jointly as the number of days from the beginning and the number of days remaining (including that day). On three successive days there were respectively 6, 5 and 3 races. Which days were these, and how long did the regatta last?

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. III. Variation, Examples III, No. 18