The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip.

If it takes 8 hours for a bus with an average velocity of 65mph to travel from Amarillo to Austin then,

d = 65 (8) = 520 miles

The distance from Amarillo to Austin (or vice versa) is 520 miles.

If the function to get the distance traveled by the automobile is given by:

d (x) = 80 t

Then, the inverse variation relationship would be

d-1 (x) = t = d / 80

Since d = 520

t = 520 / 80

t = 6.5 hours

It takes 6.5 hours for the automobile to complete the trip