"A 79 kg man is riding on a 38 kg cart traveling at a speed of 5.0 m/s. He jumps off with zero horizontal speed relative to the ground. What is the resulting change in the cart's speed, including sign? "
I have:
$$(79+38) \times5 / 28 > 15.4 - 5 = 10.4 ?$$
To answer your question, simply use law of conservation of momentum to get $$(79+38)*5=-79*5 + 38*v$$ This sould give your answer.
The - sign is there because $\vec v_{m/g}=0 $ this clearly means that the man jumped with a velocity of $5 ms^{-1}$ in the opposite direction of motion to that of cart.