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

Heat = kx/y^3

k2x/y^3 = kx/26^3

kx cancels out leaving

2/y^3 = 1/26^3

cross multiply

y^3 = 2(26^3)

take cube roots of both sides

y = 26 times cube root of 2

= about 32.76 feet

= 32.8 ft if you round to one decimal place

Answer 2

Let H = heat, w = amount of wood, and d = distance of the camper from the fire.

H = kw / d³

If d = 26, then H = kw / 26³

Find d if H remains the same and w is increased to 2w:

k(2w) / d³ = kw / 26³

Simplifying, we get 2 / d³ = 1 / 26³

So, d³ = 2(26)³. Therefore, d = 26 (³√2).