How Much Fuel and Oxidizer is Required for a Rocket to Reach 10,000 m/s?

[cryptcougar]

Homework Statement

A rocket for use in deep space is to have the capability of boosting a total load (payload plus the rocket frame and engine) of 3.10 metric tons to a speed of 10 000 m/s.
(a) It has an engine and fuel designed to produce an exhaust speed of 2000 m/s. How much fuel plus oxidizer is required?

Homework Equations

P=mv

The Attempt at a Solution

P = mv
P = (3.10 metric tons) (10,000 m/s) = 31,000 metric tons m / s

mv (total) = mv (fuel)
31,000 metric tons m /s = m (2000 m/s)

m= 15.5 metric tons

^^ This is not the correct answer.
I just don't know where to go with this anymore...

 

[lubuntu]

those two thing you wrote down as equal aren't, it would seem like you somehow need to quantify how much work a certain mass of fuel can do.