If a vertical pole 30 ft tall casts a shadow 8ft long, how long would the shadow of 40-ft pole be at the same time and place

Since it as at the same time and place.

Let x be the length of the shadow of the 40-ft pole.

The ratio from 30 and 8 would have to be the same as 40 and x.

30:8  =  40:x

30/8 = 40/x    Cross multiply

30x = 40*8

x = 40*8 / 30 = 32/3 = 10.67

Length of shadow for 40ft  is 10.67 ft.