Question

The gas mileage g (measured in mi/gal) for a particular vehicle, driven at v mi/h, is given by the formula g = 10 + 0.7v − 0.01v2, as long as v is between 10 mi/h and 65 mi/h. For what range of speeds (in mi/h) is the vehicle's mileage 22 mi/gal or better? (Enter your answer using interval notation.)

Answer 1

`[30,40]`

Explanation:

Given

`g = 10 + 0.7v - 0.01v^2`

Required

Determine v when g = 22

Substitute 22 for g;

We have:

`22 = 10 + 0.7v - 0.01v^2`

Collect Like Terms

`0.01v^2 -0.7v + 22- 10 = 0`

`0.01v^2 -0.7v + 12 = 0`

`0.01v^2 -0.4v-0.3v + 12 = 0`

`0.01v(v - 40) - 0.3(v - 40) = 0`

`(0.01v - 0.3)(v - 40) = 0`

Split:

`0.01v - 0.3= 0` or
`v - 40 = 0`

`0.01v = 0.3` or
`v = 40`

`v = 0.3/0.01` or
`v = 40`

`v = 30` or
`v = 40`

Writing as interval, we have:

`[30,40]`