What is the correct maximum altitude and flight time calculation for a rocket?

[Coffeepower]

Homework Statement

A 200kg rocket is loaded with 100kg of fuel and fired straight up. It accelerates at 30m/s^2 for 30sec and then runs out of fuel. Ignore any air resistance effects.

a. What is the maximum altitude of the rocket?
b. How long is the rocket in te air?
c. Draw a position vs. time graph of the rocket from launch to impact.

The Attempt at a Solution

http://www.angelfire.com/planet/garciarussellchem/coolpix/

The text says that the answer to (b) is 228sec. I say it is 181.69sec. what happened here?

p.s. Ignore the circled answer for (b) in the figure because it is wrong.

 

[Doc Al]

Show how you arrived at your answer. (The image is blank.)

 

[Coffeepower]

http://www.angelfire.com/planet/garciarussellchem/coolpix/

Just updated the image. Try it now.

 

[Doc Al]

In part of your calculation you use this formula, which is incorrect:
$$v_f = v_i + 2a\Delta t$$

 

[Coffeepower]

Thank you. That really helped out.

I got 227.6 = (rounded) 228sec.