48ft is correct
Fraction of pole in the ground = 1/2
Fraction of pole covered by water = 1/3
Fraction of pole in the ground and covered by water = 1/2 + 1/3 = (3 + 2)/6 = 5/6
Fraction of pole out of water = 1 - 5/6 = 1/6
Thus, one-sixth of the pole (out of water) is 8 ft.
So, total length of pole = 48 ft.
It may be noted that:
Length of pole in the ground = 48/2 = 24 ft.
Length of pole covered by water = 48/3 = 16 ft.
Length of pole out of water = 8 ft.
The problem may also be solved by setting up the following equation: x/2 + x/3 + 8 = x
where x denotes the total length of the pole in ft.
The equation may be solved as shown below.
5x/6 + 8 = x
8 = x - 5x/6 = x/6
x/6 = 8 or x = 48.