Answer
89 m
Work Step by Step
Here we use the equation $I=\frac{P}{4\pi r^{2}}$ where $I$ - Wave intensity, r - radius of the sphere
Let's apply this equation to nearer observer
$I=\frac{P}{4\pi x^{2}}-(1)$
Let's apply this equation to the far observer
$I=\frac{P}{4\pi (x+20)^{2}}-(2)$
Given that, $I_{1}=\frac{150}{100}I_{2}=\frac{3I_{2}}{2}-(3)$
(1),(2),=>(3)
$\frac{P}{4\pi x^{2}}=\frac{P}{4\pi (x+20)^{2}}\times\frac{3}{2}$
$2(x+20)^{2}=3x^{2}$
$2(x^{2}+40x+400)=3x^{2}$
$0=x^{2}-80x-800$
$x=\frac{-(-80)\pm\sqrt {(-80)^{2}-4\times1\times(-800)}}{2}$
$x=\frac{80\pm \sqrt {6400+3200}}{2}=\frac{80\pm97.98}{2}$
x should be a positive value so, we neglect the negative solution of the x. Therefore,
$x=\frac{80+97.98}{2}=89m$
