Let's break down the problem step by step.

1. Total number of participants: 60

2. First half of the race:

   • Participants who drop out: $\frac{2}{3}$ of 60 $\frac{2}{3} \times 60 = 40$
   • Participants remaining after the first half: $60 - 40 = 20$

3. Second half of the race:

   • Participants remaining from the first half: 20
   • We need to know the fraction of remaining participants who drop out. The problem statement seems to have a gap here. However, if we assume the same fraction for dropouts as in the first half (i.e., $\frac{2}{3}$), then: $\frac{2}{3} \times 20 = \frac{40}{3} \approx 13.33$ Let's round it to 13 for practical purposes.
   • Participants remaining after the second half: $20 - 13 = 7$

Therefore, assuming the same dropout rate for the second half as the first half, approximately 7 participants would finish the race.

However, since the problem statement did not specify the fraction of dropouts for the second half clearly, it's crucial to verify the details for accurate calculation.

Would you like further clarification on any part of the solution, or do you have any additional questions?

Here are 8 related questions to expand your understanding:

1. If $\frac{3}{4}$ of the participants dropped out in the first half, how many would finish?
2. How would the outcome change if only $\frac{1}{5}$ of the participants dropped out in the second half?
3. What percentage of the original participants finished the race?
4. If the race had three stages with equal drop rates, how many would remain?
5. How many participants would finish if $\frac{1}{4}$ dropped out in both halves?
6. What is the effect on the number of participants if the drop rate in the first half increases to $\frac{3}{4}$?
7. How many participants would remain if instead $\frac{1}{2}$ dropped out in both halves?
8. How would the number of finishers change if the dropout rate was different for each stage?

Tip: Always ensure to have clear and complete information for calculations involving fractions and percentages to avoid ambiguity and errors.