Short Answer 
The rankings for the participants are established by analyzing their race outcomes. Ultimately, the order is Sarah first, David second, James third, Julie fourth, and Roger last, confirming that David finished second.
Step 1: Assign Initial Rankings
Start by representing the participants Julie, Roger, James, David, and Sarah with letters: J for Julie, R for Roger, Ja for James, D for David, and S for Sarah. According to the race results:
- J < R (Julie beat Roger)
- J = 1, R = 2 (Julie is first, Roger second)
Step 2: Analyze Additional Comparisons
Next, incorporate the other participants based on the conditions given. From the statement “Julie finished after James,” we derive:
- Ja < J (James finished before Julie)
- David beat James but finished after Sarah: S < D < Ja
This leads to the understanding that the positions must be arranged accordingly based on these comparisons.
Step 3: Establish Final Rankings
By synthesizing all the comparisons, we can deduce the final ranking. Starting with the orders established:
- S < D < Ja < J < R
Therefore, assigning numerical values, we find that S = 1, D = 2, Ja = 3, J = 4, and R = 5. Thus, David finished second.