SOLUTION: Heat of a Campfire: 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 th

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Question 99670This question is from textbook College Algebra
: Heat of a Campfire: 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 he is 20 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?
Heat = H
Amount of Wood = W
Distance = D
Constant (k) w(wood) divided by distance (cubed)
Expression: heat = kw/d3
Expression set to a known equation from giving information: kw/d3
Cross multiply w * d3 = w d3 = 2w * 8000
Simplifies to: d3 = 16000
Solve for distance = d = 20 + √2
This answer doesn’t seem to satisfy the question, before? It reinforces the fact that the hiker is 20 ft away only?
This question is from textbook College Algebra

Answer by stanbon(29602) About Me  (Show Source):
You can put this solution on YOUR website!
Heat of a Campfire: 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 he is 20 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?
Heat = H
Amount of Wood = W
Distance = D
Constant (k) w(wood) divided by distance (cubed)
Expression: heat = kw/d^3
If w = 20ft the heat felt is kw/20^3
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Now we double the wood and ask how far he has to be from the fire
to feel [kw/20^3] heat.
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EQUATION:
kw/20^3 = k(2w)/d^3
Divide both sides by kw to get:
1/20^3 = 2/d^3
d^3 = 2^20^3
d = 20(2)^(1/3)= 25.198 ft.
He would have to be 25.198 ft. from the fire.
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Cheers,
Stan H.
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