You are a lifeguard and spot a distressed child $100$ meters along the shore and $60$ meters from the shore to the chjld$.$ You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of $4$ meters per second and swim at a rate of $1\mathrm{.}1$ meters per second. How far along the shore should you run before jumping into the water in order to get to the child in the least amount of time? Round your answer to three decimal places.

Hint: Consider this diagram, where $x$ represents the distance running and $y$ represents the distance swimming. Try to write $y$ in terms of $x,$ and use that to build the time as a function of $x.$