Answer:
Let d = the one-way trip
Write a time equation: time = dist/speed
time out + time back = 4.5 hrs
d/80 + d/100 = 4.5
Multiply by 400 to clear the denominators
400*d/80 + 400*d/100 = 400(4.5)
Cancel the denominators
5d + 4d = 1800
d = 1800/9
d = 200 miles max distance