Average speed= total distance/total time.

Let's assume that the distance from Carl's home to the beach was y miles and that it took Carl x hours to travel those y miles when going to the beach. So:

y/x=80
x=y/80

The problem tells us that it took Carl 1/2 an hour longer when coming back home. So:

y/x+1/2=70
y=70x+35
Plug in x=y/80 and solve for y.
y=7y/8+35
y/8=35
y=280

S=D/T

80=D/x

70=D/(x+1/2)

D=D
80x=70x+35
10x=35
x=3.5

80*3.5=280