Alyssa, Shreya and Rachel are doing 5−mile5-\text{mile} relay run. The most one person is allowed to run is 3 miles3 \text{ miles}, and every participant has to run at least 0.5 mile0.5 \text{ mile}.

Alyssa runs at 6 miles per hour6 \text{ miles per hour}, Shreya takes 480 seconds480 \text{ seconds} to run one mile and Rachel runs at 110 mile per minute\frac{1}{10} \text{ mile per minute}.

Distribute the 5 miles5 \text{ miles} among the three so they finish the race in the shortest amount of time possible. How many minutes will it take?

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