Final answer:
The speed that represents the rate of the train is 150 miles per hour.
Step-by-step explanation:
The rate of the train can be calculated by dividing the distance traveled by the time taken. In this case, the high-speed train travels 100 miles in (2)/(3) hour. To find the rate in miles per hour, we divide 100 miles by (2)/(3) hour.
100 miles ÷ (2)/(3) hour = 100 × (3/2) = 150 miles per hour
Therefore, the speed that represents the rate of the train is 150 miles per hour.