# 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. What would the equation be to set this up?

##### 1 Answer

#### Explanation:

We have some variables we need to define. There's the Heat from the fire (

And now let's build the relationship phrase by phrase (I'm going to use the symbology

The heat experienced by a hiker:

...is proportional to the amount of wood on the fire...

...and inversely proportional to the cube of the distance from the fire:

Let's see how this works. Let's set some values and then make some changes. Let's set

If we add another unit of wood, we get:

If instead we have our hiker step back 1 unit so that s/he's at distance 2, we get:

And so to compare - if the hiker wanted to sit at distance 2 from the fire but wanted to be as warm as where s/he was at distance 1, there would need to be 8 units of wood: