How long does it take to lose 40 lbs doing MMA?

the school I train at is run by a guy who puts us through a very strenuous hour. we train in a hybrid of Muay Thai, ground fighting, tkd/hapkido (korean arts program) Kali, Jeet Kune do, and we exercise alot. basically the MMA program involve the best of each art the school has to teach. I've been outta the program due to a financial rutt but soon Ima get back in the program, and I'm wondering if MMA cles @ least 3 cles (minimum) per week, will help me lose 40 lbs in a desirable amount of time, like a month or 2.