i am getting
t(x) = x/100 + (((200-x)^2 + 200^2)^1/2) /50)
as we can see if the guy swims all the way he will be going 80 000^1/2 at 50 m/min and will take him
5.66 hours appx
try x = 0 in both equations...
here i am using the starting point at the bottom left of the diagram and the x value is the horizontal distance from the towel to the point that the swimmer reaches shore
let me know what you think