We can use the definition of moment of force given by:
[tex]\tau=F\times r[/tex]Where:
τ = magnitude of the torque
F = Force
r = the distance from the point about which the torque is being measured to the point where the force is applied
For Milhouse:
[tex]\begin{gathered} \tau=24\cdot rm \\ rm=2.9-rb \\ \tau=24\cdot(2.9-rb) \end{gathered}[/tex]For Bart:
[tex]\begin{gathered} \tau=35.1\cdot rb \\ \end{gathered}[/tex]Equaling the previous equations:
[tex]\begin{gathered} 35.1\cdot rb=24(2.9-rb) \\ 35.1rb=69.6-24rb \\ 59.1rb=69.6 \\ rb=\frac{69.6}{59.1} \\ rb=1.178m \end{gathered}[/tex]Answer:
Approximately 1.178m
