The heat 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.

Question

The heat 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 the hiker is 26 ft from the fire and someone doubles the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before? (Round your answer to one decimal place.)  ft

Answer 1

H = kw / d³

H = (2w)k / 26³

H = wk / d³

So, 2wk / 26³ = wk / d³

2 / 26³ = 1 / d³

2d³ = 26³

d³ = 26³ / 2

d = 26 / (³√2) = 20.6 ft