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 16 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.)

Question

anonymous · Answer

campfire = heat. if one increases the other must also at the same rate. I'm going to be honest. I can't seem to set the second part up. If wood is doubled. Heat is doubled. I think his distance then must double. But it is a cubed distance. what do you think?

anonymous · Answer

inversely proportional means as one goes up the other must go down. That doesn't make logical sense for this situation.

anonymous · Answer

I was thinking that the equation is set up like:$$H=kw/d^3$$
With k being a constant. Not completely sure how to figure out the distance though.

anonymous · Answer

It does make logical sense because the equation it set up to give a value to the heat not the heat in relation to distance.

anonymous · Answer

ok... using ur formula Assume W and H are 1 and solve for k using 16 as d^3. Then solve for d^3 using 2 as W and H and ur new k.

anonymous · Answer

excuse me 16 as d then you still have to cube it. then solve for d after you find k

anonymous · Answer

It doesn't tell you what the constant is and in relation to the heat given off so I think you should be able to assume a basis

anonymous · Answer

Hopefully somebody else can help. Thats the best I got. I'm not good at word problems