To find out how many more miles Trey needs to run to complete the race, we first need to determine the total distance of the race.
Given that Trey has completed \( \frac{1}{4} \) of the race and has run 1.2 miles, we can set up the equation:
\[ \frac{1}{4} \text{ of the total distance} = 1.2 \text{ miles} \]
Let \( d \) be the total distance of the race. Then we can express this as:
\[ \frac{1}{4} d = 1.2 \]
To find \( d \), we can multiply both sides of the equation by 4:
\[ d = 1.2 \times 4 \]
Calculating that gives:
\[ d = 4.8 \text{ miles} \]
Now that we have the total distance of the race, we can find out how much distance Trey 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. We can calculate how many miles that is:
\[ \frac{3}{4} \text{ of the total distance} = \frac{3}{4} \times 4.8 \]
Calculating that gives:
\[ \frac{3}{4} \times 4.8 = 3.6 \text{ miles} \]
Therefore, to complete the race, Trey must run:
\[ \boxed{3.6} \text{ miles} \]
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