Question

Due to wind resistance, a car's gas mileage is inversely proportional to the square of its highway driving speed. A particular car gets 32 miles per gallon at a speed of 65 miles per hour. What gas mileage would it get for a speed of 75 miles per hour?

Answer 1

\[milage \alpha \frac{1}{speed^{2}}\]
where the alpha symbol mean proportional and the fraction gives you the inverse
(ie as the speed goes up the mileage goes down)

Answer 2

you can replace the alpha with and equals sign if you introduce a constant of proportionality:\[mileage = \frac{c}{speed^{2}}\]

Answer 3

By direct subtitution you can solve first the constance value of c (using the known values of 32mpg and 65mph).
You can then use that same constant along with 75 mph to find the unknown mileage of the quesiton.

Answer 4

thanks :)