a) The equation solve for x is 3/4x - 1/3x = 2 1/2.
b) The position of the ant relative to the ground level, x is 6 inches.
c) The distance between where the ant is and where the beetle is, is 3 1/2 inches.
How the equation to determine x is derived.
a) The equation representing the position of the ant relative to the ground level x can be expressed as:
Assume the ant's position is the lowest below the ground, x
Beetle intial position= 3/4x
After climbing 1/3x it's new position = 2 1/2
The equation solve for x is
3/4x - 1/3x = 2 1/2
b) Solving the equation:
3/4x - 1/3x = 2 1/2
3/4x - 1/3x = 5/2
LCM is 12
9x - 4x = 30
5x = 30
x = 30/5 = 6
So, the position of the ant relative to the ground level, x is 6 inches.
C) The distance between where the ant is and where the beetle is can be found by subtracting the position of the beetle from the position of the ant:
The ant's position is 6 inches
The beetle intial position is 3/4 * 6 = 4.5 inches
After climbing 1/3x = 1/3 * 6 = 2 inches
New position of beetle is 4.5 - 2 = 2.5
The distance between the ant position and beetle position is 6 - 2.5 = 3.5 inches.
So, the distance between where the ant is and where the beetle is, is 3 1/2 inches.