It looks more like Alternaria or Early Blight than Late Blight.
(Late Blight usually kills the whole plant in a week, so it is
kind of hard to miss on a plant with an advanced case.)
You can look at pictures of tomato leaf diseases at these
URLs:
http://aggie-horticulture.tamu.edu/p...emsolver/leaf/
http://vegetablemdonline.ppath.corne...omLeafKey.html
http://vegdis.cas.psu.edu/VegDisases.../tomatodis.htm
This document has pictures of nutrient deficiency symptoms:
http://4e.plantphys.net/article.php?ch=5&id=289
You could try cutting off all of the diseased leaves and then
spraying the plants with a 6% Clorox solution (laundry bleach
in water; one measure of laundry bleach for 16 and 2/3rds
measures of water). If more leaves die after spraying, that
simply means that they were already infected, even if the
symptoms were not obvious yet. That should keep the disease
from spreading to leaves and plants that are not yet infected.
You might give a light spray to the soil underneath them, too,
since the leaves may be getting it from splash-up from the
rain.
Another option is to use a hydrogen peroxide spray instead of
laundry bleach:
http://www.using-hydrogen-peroxide.c...-peroxide.html
In either case, you probably cannot save the already diseased
leaves. If you cut off the diseased leaves, spray, and nothing
happens (the disease seems to still be there on new leaves),
then it may be a soil mineral deficiency (those usually include
other symptoms as well as leaf symptoms, one way to tell them
from bacterial or fungal leaf diseases). It may also mean that
the disease is being blown in on the wind from infected weeds
somewhere nearby, or that insects are carrying it.