Mahira and Neelima started walking towards each other, simultaneously from Gandhi Nagar and Nehru Nagar respectively, which are $72$ miles apart. They met after $6$ hours. After their meeting, Mahira reduced her speed by $1$ mile/h and Neelima increased by $1$ mile/h. They arrived at Nehru Nagar and Gandhi Nagar respectively at the same time. Find their initial speeds :