A 240V 24A charger which is much more common, and which is not paid for by Tesla so has its own terms, can recharge 18 miles of range per hour of charge, so 13 hours are needed for a full recharge.
A 240V 40A charger can recharge 31 miles of range per hour of charge, so 8 hours are needed for a full recharge.
Tesla also notably recommended that people drive low speeds on long trips to increase the chances they will see ranges of 240 miles as opposed to the 170 or so that seems to be under more typical driving conditions.
When one is off of the Tesla routes on the west and east coast, and driving a steady 60mph without climate control, one can travel 240 miles per 12 hour period if they have access to the higher capacity 240V/40A charger exactly every 240 miles (20 mph average speed), or 240 miles per 17 hours with the 240V/20A station (14.1 mph average speed). This is assuming there is no cold weather. If there is cold weather or faster driving, that reduces to a 170 mile range per 12 or 17 hour period (10-14mph average).
Tesla plans to address this with a nationwide network of Supercharger stations which will reduce the full recharge time dramatically, at the cost of shorter battery life.
Tesla claims that all energy for the network, which requires the ability to deliver to 4 cars simultaneously in 1 hour about 100kWh total of power per 85kWh capacity charge, will run exclusively on a small 30 kW max rated capacity installation of solar powered panels at each 4 car charge station and that customers will not only "Drive for Free. Forever. On Sunlight.”, but stations will produce a surplus of energy that will be sold at a profit.
source for recharge times: http://www.teslamotors.com/charging#/outlet
source for solar powered car claims: http://www.visualnews.com/2012/09/26/tesla-electric-cars-dri...