1. **State the problem:** Helen finished a race in 516.06 seconds. Her brother finished 6.46 seconds after Helen. We need to find how long it took Helen's brother to finish the race. 2. **Formula used:** To find the brother's time, add the time difference to Helen's time. $$\text{Brother's time} = \text{Helen's time} + \text{Time difference}$$ 3. **Substitute the values:** $$\text{Brother's time} = 516.06 + 6.46$$ 4. **Calculate:** $$\text{Brother's time} = 522.52$$ 5. **Answer:** Helen's brother took 522.52 seconds to run the race.