Question

Solve the problem as directed. 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. a0 hours

Answer 1

The automobile would take 6.5 hours to complete the trip.

Explanation:

This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:

Inverse variation equation:
`x1y1=x2y2`

`x1`: speed of the bus, 65 miles per hour

`y1`: time to Austin by bus, 8 hours

`x2`: speed of the automobile, 80 miles per hour

`y2`: time to Austin by automobile, unknown

Now we can replace the values in the equation and clear
`y2`, this is:

`65*8=80*y2\\y2=(65*8)/(80) =(520)/(80) =6.5\\`

The automobile would take 6.5 hours to complete the trip.

Answer 2

65*8 = 520 miles traveled

520/80 = 6.5 hours for the car