If Trey has completed \( \frac{1}{4} \) of the race and has already run 1.2 miles, we can find the total distance of the race.
Let \( D \) be the total distance of the race. Since \( \frac{1}{4} \) of the race is 1.2 miles, we can set up the equation:
\[ \frac{1}{4}D = 1.2 \]
To find \( D \), we can multiply both sides of the equation by 4:
\[ D = 1.2 \times 4 = 4.8 \text{ miles} \]
Now, to find out how many more miles Trey needs to run, we need to determine how much he has left to run:
Since he has completed \( \frac{1}{4} \) of the race, he has \( \frac{3}{4} \) of the race left to run.
To find the remaining distance:
\[ \text{Remaining distance} = D - \text{distance already run} = 4.8 - 1.2 = 3.6 \text{ miles} \]
So, Trey must run 3.6 more miles to complete the race.