Here is a quick and dirty system I made for running a foot race.
Step 1 - Determining the Course: Roll 6D6. Each die represents a part of the race. For each even die, that portion of the course favors raw speed, so characters will make strength rolls; for each odd number, that portion of the course is narrow, uneven, obstructed, and/or twisting, so players will be making dexterity rolls.
Step 2 - Running the Race: Players and NPCs make rolls to pass each section of the race. Exact order of racers is determined by how far over or under the target DC they roll. After completing 2 consecutive sections of course that favor the same stat, racers make a constitution roll which increases in difficulty by 3 for every consecutive section of course favoring the same stat. Failure means the next STR or DEX roll is HARD.
Step 3 - Determine the Winner: The winner is the racer with the most successes, or if their is a tie with number of successes, the racer whom exceeded the DC by the most. For example, if 2 racers both have 3 successes; racer A beat the target by 1, 3, and 4 - net 8; racer B beat the target by 2, 3, and 1 - net 6, so racer A wins!