In a race, people rode either bicycles with blue wheels or tricycles with tan wheels. Given that 15 more people rode bicycles than tricycles and there were 15 more tan wheels than blue wheels, what is the total number of people who rode in the race?
1. Let \( b \) be the number of bicycles and \( t \) be the number of tricycles.
2. According to the problem, there are 15 more people who rode bicycles than tricycles. This can be written as:
   \[
   b = t + 15
   \]
3. Each bicycle has 2 blue wheels and each tricycle has 3 tan wheels. The problem states that there are 15 more tan wheels than blue wheels. This can be written as:
   \[
   3t = 2b + 15
   \]
4. Substitute \( b = t + 15 \) into the equation \( 3t = 2b + 15 \):
   \[
   3t = 2(t + 15) + 15
   \]
5. Simplify the equation:
   \[
   3t = 2t + 30 + 15
   \]
   \[
   3t = 2t + 45
   \]
6. Subtract \( 2t \) from both sides:
   \[
   t = 45
   \]
7. Substitute \( t = 45 \) back into the equation \( b = t + 15 \):
   \[
   b = 45 + 15
   \]
   \[
   b = 60
   \]
8. The total number of people who rode in the race is the sum of the number of people who rode bicycles and the number of people who rode tricycles:
   \[
   b + t = 60 + 45
   \]
   \[
   b + t = 105
   \]

The final answer is \(\boxed{105}\).