The internet has suffered from large forms of insecurity ranging from scamming, hacking and theft of information. Lately the use of CAPTCHAs has become a common security tool for authentication and authorization. However CAPTCHAS has suffered from certain vulnerabilities in the context of the simplicity offered by the challenge-response scenario and its timing which leaves room for improvement. This paper proposes a Time-Out Multiple Challenge-Response (C-R) CAPTCHA Framework that Utilizes Mathematical Modelling as a basis for overcoming some of the challenges faced by current CAPTCHA Systems. Our approach ensures security during the authorization and authentication process