Trey has completed \( \frac{1}{4} \) of the race and has run 1.2 miles. To find the total distance of the race, we can set up the equation:
\[ \frac{1}{4} \times \text{Total Distance} = 1.2 \text{ miles} \]
Let \( D \) be the total distance of the race. Then,
\[ \frac{1}{4} D = 1.2 \]
To solve for \( D \), 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 find out how much more Trey has to run. He has already run 1.2 miles, so the remaining distance is:
\[ \text{Remaining Distance} = D - 1.2 = 4.8 - 1.2 = 3.6 \text{ miles} \]
Thus, Trey must run 3.6 miles more to complete the race.
The answer is 3.6.