The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as the other, are placed 14 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (Round your answer to two decimal places.)

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.

I = s/d^2

The object is placed between the sources which are 14 feet apart

at a point where

Week = strong

s/x^2 = 3s/(14 - x)^2

cross multiply

(14 - x^2)s = 3sx^2

Divide both sides by s

(14 - x)^2 = 3x^2

Expand

196 - 28x + x^2 = 3x^2

subtract (196 - 28x + x^2) from both sides

2x^2 +28x - 196 = 0

Divide both sides by 2

x^2 + 14x - 98 = 0

Solve using quadratic equation

(work not shown)

x = {-19.1244, 5.12436}

disregard the negative root since the distance cannot be negative

x = 5.12436

14 - x = 8.87564

Rounded

8.88 feet