Short Answer 
The train is traveling 120 miles at an average speed of 80 mph but stops for 16 minutes after covering one-third of the distance. By setting up and solving the equation, we find that the average speed of the train is 60 mph.
Step 1: Understand the Problem
In this problem, we are dealing with a train traveling between two stations that are 120 miles apart. The average speed of the train is given as 80 mph. However, the train stops for 16 minutes, during which it covers only 1/3 of its journey before stopping. We need to establish the relationship between the distance covered, speed, and time taken to formulate an equation.
Step 2: Set Up the Equation
Let the train’s average speed be x mph. To set up the equations, consider the total time taken for the journey without stops compared to the time with the stop. The equations include:
- Total time without stop: 120/x hours.
- Time before stopping: (1/3 * 120)/x = 40/x hours.
- Time taken after stopping: 80/(x+15) hours (change in speed due to stop).
Combine these to form the equation: 40/x + 16/60 + 80/(x+15) = 120/x.
Step 3: Solve the Equation
To find the average speed, rearrange the equation and simplify it. This leads us to:
- 80(1/x – 1/(x+15)) = 8/30.
- This simplifies to x^2 + 15x – 450 = 0.
By factoring, we find (x + 75)(x – 60) = 0, giving us solutions for x as 60 mph (since speed cannot be negative). Therefore, the required average speed of the train is 60 mph.