Question 102105
The gravitational force between two objects varies inversely as the square of the distance between the objects.  If a force of 25 pounds results from two objects that are 6 miles apart, how much force results from two objects that are 15 miles apart?

The force varies inversely as the square of the distance or
{{{F[g]=k/r^2}}} where k is a constant or re-arranged 
{{{F[g]*r^2 = k}}}
Set up a ratio :
{{{F[1]*(d[1])^2=F[2]*(d[2])^2}}}
{{{25*6^2=F[2]*15^2}}} Plug in what you know. 
{{{25*6^2/(15^2)=F[2]*cross(15^2)/cross(15^2)}}} Multiply by multiplicative inverse of (15^2) or 1/(15^2).
{{{F[2]=5^2*(2*3)^2/(3*5)^2)}}}
{{{F[2]=cross(5^2)*(2*cross(3))^2/(cross(3)*cross(5))^2)}}}
{{{F[2]=4}}}
Final answer, F = 4 lbs.