Each cyclist enters the section at the bottom left corner (point A) and must exit at the top right corner (point B), but otherwise may take any route between the two points.

As a cyclist in the race, you know that you can cycle at a constant speed of 30mph on tarmac, but only at half that speed (15mph) on grass. By taking the optimum route, how long will it take you to cycle from point A to point B?

(For the purposes of this question it is assumed that you enter at point A travelling at 15mph and in transitioning from the grass surface to tarmac, the time taken to accelerate from 15mph to 30mph is zero)