River crossing - solve the problem

What is the length of AC in terms of x?

• the time taken to swim from A to C.

• the time taken to run from C to D.

Hence write down an expression for the time taken, T, to travel from A to D in terms of x.

Find

Now solve

to determine the value of x that minimises the time taken.

How do you know this is a valid value?

For this value of x, find the minimum time possible and descibe the route.