The intensity of light (in foot-candles) Varies inversely as the square of X, the distance in feet from the light source.

Question

The intensity of light 3 feet from the source is 96 foot-candles. How far away is the source if the intensity of light is 6 foot-candles?

Answer 1

I = k/x^2

96 = k/3^2

96 = k/9

k = 864

I = 864/x^2

When I = 6

6 = 864/x^2

Cross multiplies:

6x^2 = 864

x^2 = 144

x = 12

The light source is 12 feet away when the intensity is 6 foot/candles