A family decides to go to the lake on their summer vacation. Their child is small, just around 4 or 5 years old and is very excited. When they get to the lake, the child runs immediately into the water while his parents set up their blanket on a little beach by the lake. Out in the lake, the child steps on a rock, hurts his toe, and begins to cry for his mom to come get him.
$v_s=3~m/s$ on the sand and $v_w=1~m/s$ in the water. The distance between the mom and the child is given in the figure, with $d=30~m$, $a=10~m$ and $b=30~m$. What's the minimum time **in seconds** for her to reach her child?

**Details and assumptions**

- Remember, the quickest path between 2 points on a plane is a straight line (if you travel at constant velocity).
- There are a couple ways to do this problem, but one straightforward way involves solving a quartic equation, which you can do here.