To find out how many more miles Trey must run to complete the race, we first need to determine the total distance of the race.
Since Trey has completed \( \frac{1}{4} \) of the race and he has run 1.2 miles, we can set up the following equation:
\[ \frac{1}{4} \text{ of total distance} = 1.2 \text{ miles} \]
Let \( D \) be the total distance of the race. This gives us:
\[ \frac{1}{4} D = 1.2 \]
To find the total distance \( D \), we multiply both sides of the equation 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 the distance Trey has left to run. He has completed \( 1.2 \) miles, so the remaining distance is:
\[ D - 1.2 = 4.8 - 1.2 = 3.6 \text{ miles} \]
Therefore, Trey must run 3.6 miles more to complete the race.
The answer is 3.6 miles.