Answer
She can travel in the interval of $[0, 60]$
$0\leq v \leq 60$
Work Step by Step
We have to find range of speed where stopping distance is less than or equal to $240ft.$
It means, that we have to find : $d \leq 240$
$v+\frac{v^2}{20}\leq 240$
$v+\frac{v^2}{20}-240\leq 0$
We can write it as a quadratic equation and then solve it using interval notation:
$v+\frac{v^2}{20}-240= 0$
$v^2+20v-4800=0$
$v_1=-80$ ; $v_2=60$
We have three possible interval:
$(-\infty, -80]$ - Positive
$[-80, 60]$ - Negative
$[60, +\infty)$ - Positive
Note, we're looking for interval where it is less than or equal to $0$, so the answer is second interval:
$[-80, 60]$
But, we also have to note that we're looking for interval of range of speeds. and speed cannot be negative number. So the actual interval of speed will be: $[0, 60]$
$0\leq v \leq 60$
