1. **State the problem:** Ricardo ran a 400-meter race 3 times. His fastest time was 54.3 seconds, his slowest time was 56.1 seconds, and his average time was 55.0 seconds. We need to find his time for the third race. 2. **Formula used:** The average time is calculated by dividing the sum of all times by the number of races. $$\text{Average} = \frac{\text{Sum of all times}}{\text{Number of races}}$$ 3. **Set up the equation:** Let the time for the third race be $x$ seconds. $$55.0 = \frac{54.3 + 56.1 + x}{3}$$ 4. **Multiply both sides by 3 to eliminate the denominator:** $$3 \times 55.0 = 54.3 + 56.1 + x$$ $$165.0 = 54.3 + 56.1 + x$$ 5. **Add the known times:** $$165.0 = 110.4 + x$$ 6. **Subtract 110.4 from both sides to solve for $x$:** $$165.0 - \cancel{110.4} = \cancel{110.4} + x - 110.4$$ $$54.6 = x$$ 7. **Answer:** Ricardo's time for the third race was $54.6$ seconds.