If Trey has completed \( \frac{1}{4} \) of the race and has run 1.2 miles, we can find the total distance of the race.
Let the total distance of the race be \( d \) miles. Since \( \frac{1}{4} \) of the race is 1.2 miles, we can write the equation:
\[ \frac{1}{4}d = 1.2 \]
To find \( d \), 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 calculate how much farther Trey needs to run to complete the race. He has completed \( \frac{1}{4} \) of the race, which is 1.2 miles, so he has:
\[ d - \text{distance already run} = 4.8 \text{ miles} - 1.2 \text{ miles} = 3.6 \text{ miles} \]
Therefore, Trey must run 3.6 miles to complete the race.
The answer is 3.6 miles.