Murry, Just one simple equation is required...

(1/focal length) = (1/object distance) + (1/image distance)

let's use the following short hand notation:

1/f = 1/ob + 1/im

In your question, the image distance is unknown and the object distance is infinity....

so, at the short end of the zoom range the focal length is 50mm so...

1/50 = 1/<infinity> + 1/im

I get an image distance of 50mm...

and I guess at the other end of the zoom range the focal length is 150mm - right?

so you'll need an image distance of 150mm to focus the 150mm focal length at infinity (this is the case, by definition for all 150mm focal legth lenses!)

bottom line, you need to get the rear nodal plane of the lens within 50mm of the film plane to focus at infinity.

further, to focus this lens at 18 feet (let's call it 5486mm)...

1/50 = 1/5486 + 1/im

---> im = 50.46 mm

so, when the 50mm lens is focused at 18 feet (==5486 mm), the rear nodal plane of the lens is about 50.46 mm from the film plane. So to focus this lens at infinity, you just need to be able to get it another half a millimeter closer to the film.

Hope this helps...