Three students push horizontally on a large $80$ kg crate sitting on the floor. Two of them push to the left on the crate, each with a force of $170$ N $.$ The third pushes to the right on the crate with a force of $150$ N$.$ Assume that no friction acts on the crate. $$

$($a$)$ What is the acceleration of the crate?

$($b$)$ What will happen to the net force and acceleration if a fourth student jumps on top of the crate? Explain your reasoning.