physics
posted by steve .
In 2003, New Zealand households consumed a total of 153.6E+15 J of energy (the largest amount of any sector in the New Zealand economy). How many days would it take for the sun to put that amount of energy onto a region 20.0 km by 20.0 km (0.15 percent of New Zealand's total land area)? Assume that energy from the sun arrives at the surface of the earth with an average intensity of 1000.0 W/m2

Multiply 1000 W/m^2 by the area in square meters. (20*10^3 m)^2
That would be the amount of energy received per second by the country's solar panels.
P = 4.00*10^11 W (Note that this power is only delivered during daylight, close to the middle of the day, on relatively clear days.)
Number of seconds to receive 153.6*10^15 J of energy (total national household demand), at that power, is
P = 3.84*10^5 s
That equals 4.44 days. Since the sun doesn't shine all day long, a more accurate value would be 10 days.