A helicopter makes a round trip flight that lasts 4.5 hrs. if the average rate out was 80 miles per hour and the average rate in was 100 miles per hour. what was the helicopters greatest distance from the airport?

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