Roy needs to travel from $A$ to $C.$

In order to do this, he will swim to the point $B$ and run the rest of the way.

(You can move the point $B$ to help visualise the problem.)

Roy can swim at $1.2{\text{ms}}^{-1}$ and run at $5{\text{ms}}^{-1}.$

Find the shortest possible time it could take Roy to travel from $A$ to $C.$

(You are given that the stationary value for total time gives a minimum.)

Let the horizontal distance from $A$ to $C$ be called $x$. Then $BC=70-x$.

Calculate the distance $AC$ in terms of $x$.

The total time take is equal to the time taken from $A$ to $C$ plus the time take from $B$ to $C$. Express the total time as a function of $x$ and use differentiation to find the optimum $x$ which minimises the total time.

Give your answer to the nearest second.