If Trey has completed \( \frac{1}{4} \) of the race and has run 1.2 miles, then we can find the total length of the race and the remaining distance he must run.
Let \( d \) be the total distance of the race. Since he has completed \( \frac{1}{4} \) of the race:
\[ \frac{1}{4}d = 1.2 \text{ miles} \]
To find \( d \), we can multiply both sides by 4:
\[ d = 1.2 \times 4 = 4.8 \text{ miles} \]
Now that we know the total distance of the race is 4.8 miles, we can find out how much more distance he needs to run to complete the race. He has already run 1.2 miles, so the remaining distance is:
\[ d - 1.2 = 4.8 - 1.2 = 3.6 \text{ miles} \]
Therefore, Trey needs to run 3.6 miles more to complete the race.