Respuesta :
Given:
Initially, the beetle is 3/4 inch below ground level.
The beetle climbs 1/3 the distance the ant is below ground level.
Finally, the beetle is now 2 1/2 inches below ground level.
Explanation:
a) To find: The equation
Let x be the position of the ant relative to ground level.
According to the question,
The equation is,
[tex]\frac{1}{3}x=2\frac{1}{2}-\frac{3}{4}[/tex]b) To solve for x:
On solving we get,
[tex]\begin{gathered} \frac{1}{3}x=\frac{5}{2}-\frac{3}{4} \\ \frac{1}{3}x=\frac{7}{4} \\ x=\frac{21}{4} \\ x=5\frac{1}{4} \end{gathered}[/tex]Therefore, the position of the ant relative to ground level is
[tex]5\frac{1}{4}inches[/tex]c) To find: The distance between the ant and beetle.
The distance will be,
[tex]\begin{gathered} d=5\frac{1}{4}-2\frac{1}{2} \\ =\frac{21}{4}-\frac{5}{2} \\ =\frac{11}{4} \\ d=2\frac{3}{4}inches \end{gathered}[/tex]Therefore, the distance between them is,
[tex]2\frac{3}{4}inches[/tex]