If you follow this link (like Foster gave you), you can see the route and the how many miles each track segment is:
http://test.dualsportmaps.com/?link=102895
It's 7 miles of pavement from Leavenworth up to the start of the River Road. Figure 15 minutes.
It's 14 miles of dirt river road to Atchison plus another few miles of city pavement to get into Atchison. Figure less than 45 minutes--depends on how many breaks and how long they are. If it's muddy, all bets are off!
It's 23 miles of dirt roads (and some gravel) from Atchison to Wathena. With a few photo stops, etc, figure at least an hour. If it's muddy, it will be the end of the ride most likely!
After that...it's over 30 mile of mostly dirt roads up to White Cloud...another hour+.
The route we ran last time is 43 miles back to Atchison....2 hours.
Flat tires, mechanical failure, lose a rider....time can dramatically change!