Analytical Applications of Differentiation · Superchallenge problem

A lifeguard sits on the beach $30$ m from a straight shoreline. A swimmer in trouble is $40$ m out from the shoreline, and the point of the shoreline nearest the swimmer is $70$ m (measured along the shoreline) from the point nearest the lifeguard. The lifeguard runs at $4$ m/s on sand and swims at $3$ m/s. Find the least possible time, in seconds, for the lifeguard to reach the swimmer.