To determine how many more miles Trey must run to complete the race, first we need to find the total distance of the race.
Since Trey has completed \( \frac{1}{4} \) of the race and has run 1.2 miles, we can set up the equation:
\[ \frac{1}{4} \text{ of Total Distance} = 1.2 \text{ miles} \]
To find the total distance, we can multiply both sides by 4:
\[ \text{Total Distance} = 1.2 \times 4 = 4.8 \text{ miles} \]
Now, we need to find out how much more Trey needs to run. Since he has completed \( \frac{1}{4} \) of the race, he has \( \frac{3}{4} \) of the race left to run. We can calculate \( \frac{3}{4} \) of the total distance:
\[ \frac{3}{4} \text{ of Total Distance} = \frac{3}{4} \times 4.8 \text{ miles} = 3.6 \text{ miles} \]
Therefore, Trey must run 3.6 miles more to complete the race.
Answer: 3.6 miles