2 guys dig a ditch

Um...

x + y = 100 feet

x=100-y

.75x + 1.25y = $100

.75(100-y) + 1.25y = 100
75 - .75y + 1.25y = 100
.5y = 25
y = 50

They each dig 50 feet.

.75 (50) + 1.25 (50) = 37.5 + 62.5 = 100

???

Say it again?

A gets paid $1.25 per foot
B gets paid $0.75 per foot
To get $50, A has to dig 50/1.25 feet, which = 40 ft.
To get $50, B has to dig 50/0.75 feet, which = 66.67 ft.
But there is only 60 ft left after A has dug his $50 worth. B can only dig $45 worth.