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Google scientists published Bottleneck Bandwidth and Round-trip propagation time (BBR), a novel TCP congestion control algorithm variant. Unlike traditional congestion control algorithms, BBR adjusts its transmission rates by periodically measuring the network traffic based on round-trip propagation time (RTprop) and available bottleneck bandwidth (Btlbw). This results in BBR achieving higher delivery rates and minimizing the latency on our modern-day network infrastructure. However, some recent experimental evaluations and analyses have shown severe RTT (round-trip time) fairness concerns in the TCP-BBR algorithm. When two competing flows with different RTTs coexist on a shared bottleneck link, BBR tends to prefer and favor longer RTT flows, therefore consuming more bandwidth share than short RTT counterparts, which can result in short RTT flows being starved even to death. This preference nature of the BBR in favor of long RTT flows results in an acute throughput imbalance and an extreme BBR and network vulnerability that malevolent individuals can easily exploit by increasing the delay (RTTs) in their flows to create unwarranted long RTTs on their TCP flows to unfairly obtain and enjoy the lion's share of the available bandwidth than the rest of users on the network. The BBR-With Adaptive Pacing Gain Rates (BBR-APG) algorithm is proposed in this study as an alternative solution to the TCP-BBR's RTT fairness problem. Our proposed approach adaptively adjusts the pacing gain rates of each TCP flow based on the bottleneck inflight queue status during the bandwidth estimation phase instead of the default fixed pacing gain rates as provided by the original version of the BBR algorithm, which only works perfectly when only a single flow is involved. With the BBR-APG algorithm, different RTT flows can fairly compete for the available bottleneck bandwidth, thus enhancing the RTT fairness issue that has been compromised in the original version of the BBR algorithm. Through our extensive simulation analysis on NS3, we identified that our proposed methodology improves RTT fairness by more than 18\%, a reduction of more than 24\% and 20\% on packets retransmission rates and queuing delay, respectively, compared to other recently published BBR variants like an adaptive congestion window of BBR (BBR-ACW) on various network conditions.