Algebra 2 question?

Question

The heatt experienced by a hiker at a campfire is proportional to the amount of wood on the fire, and inversely proportional to the cube of his distance from the fire. If he is 20ft from the fire, and someone doubles the amount of wood burning, how far from the fire would have to be so that he feels the same heat as before?

So far I got this H = x W/d

H= heat
w= wood
d= distance

and then I got this H = x w^2/20^3

Ok what do I do now?

Answer 1

The proportionality statement means:
h = Kw/d^3 , where K is some constant.
In this case you want h(before) = h(after)
h(before) = h(after)
Kw/(20)^3 = K(2w)/d^3
1/(20)^3 = 2/d^3
d^3 = 2(20)^3
d = 20cube root(2)
d = 25.198ft