After noting down the odometer reading, that showed smallest four digit square number, Rimzim started driving to school with constant speed at $9 A.M$. After one hour, he observed the delay in reaching school and doubled the speed to reach at $11 A.M$. In school parking, he again noticed odometer which showed the number that reads same from both sides. What was the speed of Rimzim at $9.50 A.M ?$ (round to one decimal place)