Answer:
Speed of first train = 36 mph
Speed of second train = 60 mph
Step-by-step explanation:
Given:
First train leaves Cincinnati at 2:00 PM
Second train leaves same station at 4:00 PM
Speed of second train is 24 mph faster than first train.
The second train overtakes the first at 7:00 PM
To find the speeds of each train.
Solution:
First train:
Let speed of first train be = 
Time of travel between 2:00 PM to 7:00 PM = 
Distance traveled by 1st train in 5 hours in miles = 
Second train:
Then, speed of second train will be = 
Time of travel between 4:00 PM to 7:00 PM =
Distance traveled by second train in 3 hours in miles = 
At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.
Thus, we have:

Solving for 
Subtracting both sides by 


Dividing both sides by 2.

∴ 
Speed of first train = 36 mph
Speed of second train =
60 mph