Answer:
266.67 miles per hour.
Explanation:
Let's call the speed of Train B "x" (in miles per hour). We can start by using the formula:
distance = rate x time
Let's call the distance that Train A travels before Train B catches up "d". We know that Train A travels for 5 hours at a speed of 80 miles per hour, so its distance traveled is:
d = 80 x 5 = 400 miles
Now let's consider Train B. We know that it travels for 5 - p hours (where "p" is the number of hours it takes Train B to catch up with Train A) at a speed of "x" miles per hour. Its distance traveled is:
d = x(5 - p)
Since Train B catches up with Train A when they have both traveled the same distance, we can set these two expressions for "d" equal to each other:
80 x 5 = x(5 - p)
Simplifying this expression:
400 = 5x - xp
We don't know the value of "p", but we can use another piece of information from the problem to solve for it. We know that Train B leaves the station at some time "p.m." after noon. This means that it travels for "12 + p" hours, since there are 12 hours between noon and midnight. So we can write:
5 - p = 12 + p
Simplifying this expression:
p = 3.5
Now we can substitute this value of "p" into our equation for "x":
400 = 5x - (3.5)x
Simplifying this expression:
400 = 1.5x
Dividing both sides by 1.5:
x = 266.67
Therefore, Train B is traveling at a speed of approximately 266.67 miles per hour.