A train typically travels at a constant speed to complete a journey. Today, due to an initial delay, the train traveled the first $\frac{1}{3}$ of the journey at $\frac{1}{2}$ its normal speed. To arrive at its destination in the usual amount of time, the train had to travel the remaining $\frac{2}{3}$ of the journey at a speed of 90 miles per hour. What is the train's normal speed, in miles per hour?