Build me a booking system in PHP

We have a system called 'The Brain'. It's designed to automate my client's business. He runs a music academy and has tutors which teach certain instruments, in certain locations and rooms. We're building a system which will book people into '15 minute slots' and should NEVER be double booked. I suspect you'll have a lot of questions about this, so feel free to ask. It's got a lot of components but is fairly simple in nature. I'd like you to be a very quick worker, have a good work ethic and be VERY good at english (if you're not). A phone call may be required to explain the elements of this system easier. The deadline is 14 days which is a tall order but possible if you work hard. ## Deliverables Please READ THE ENTIRE SPEC SHEET. Ask any questions you have, please be sure you can do this as I don't want anyone's time to be wasted.