Finding time when rocket engine fails at 1055 m/s

[Jregan]

Homework Statement

A rocket accelerates vertically with a constant acceleration of 21.1m/s/s until it’s engine fails after 50 seconds. The rocket reaches an altitude of 26375m when the engine fails. When does the rocket reach its max height? (Ignoring air resistance)
I don’t understand how the equations given in the hint work with this question.

Relevant Equations

The hint says vi=a*delta t and vf=vi-g*delta t

21.1*50=1055
1055m/s is the velocity when the engine fails.
I don’t know what the time should be in the second equation.

 

[TSny]

21.1*50=1055
1055m/s is the velocity when the engine fails.

Good. Take the instant that the engine fails to be the beginning of the second phase of the motion.