To find out how many days Rose needs to spend on vacation before she takes 11 pictures, we can use the given equation:
\[ p = 11d \]
We want to find \(d\) when \(p = 11\):
\[ 11 = 11d \]
To solve for \(d\), divide both sides of the equation by 11:
\[ d = \frac{11}{11} \] \[ d = 1 \]
So, Rose will have to spend 1 day on vacation before she will have taken 11 pictures.