So, if we know that they rode the first 10 miles at the rate of 12 miles per hour, we know that they rode the first part in 50 minutes (10/12*60=50). This leaves half an hour to ride the next 12 miles. 12/(1/2)=24. So, if I didn't mess anything up, they should have traveled the last part at twice their initial speed, at 24 miles per hour.