First I will assume 4.5 hours to mean 4 hours and 30 minutes.
270 / 3 = 90 mph
The train is cruising at 90 mph
So in 1 minute the train will travel:
90 / 60 = 1.5 miles
In 1 minute the trail will travel 1.5 miles.
Therefore:
In 4 hours the train will travel:
90 * 4 = 360 miles
In 30 minutes the train will travel:
30 * 1.5 = 45 miles
Therefore:
360 + 45 = 405 miles