It is inevitable that our lives will be busy because of service to God and people. But busy lives doesn’t mean busy hearts, as Paul Miller suggests:
The quest for a contemplative life can actually be self-absorbed, focused on my quiet and me. If we love people and have the power to help, then we are going to be busy. Learning to pray doesn’t offer us a less busy life; it offers us a less busy heart. In the midst of outer busyness we can develop an inner quiet. Because we are less hectic on the inside, we have a greater capacity to love… and thus to be busy, which in turn drives us even more into a life of prayer. By spending time with our Father in prayer, we integrate our lives with his, with what he is doing in us. Our lives become more coherent. They feel calmer, more ordered, even in the midst of confusion and pressure.
Paul Miller, A Praying Life