A ferryboat on a river has a speed v relative to the water. The water of the the river flows with a speed V relative to the ground. The width of the river is d. (a) Show that the ferryboat takes a time 2d/p v2 − V 2 to travel across the river and back. (b) Show that the ferryboat takes a time 2dv/(v2 − V 2) to travel a distance d up the river and back. Which trip takes the shorter time?