Short Answer 
Mr. Johnson travels 180 miles in 7.5 hours at a speed of 24 miles per hour. To catch him, James, who has a 2.5-hour delay, must travel at 36 miles per hour for 5 hours.
Step 1: Calculate Mr. Johnson’s Distance
First, we need to determine how far Mr. Johnson travels in one hour. Given that he covers 24 miles in an hour, we can calculate the distance he travels in the total time he is on the road. Since his son James starts chasing after a delay of 2.5 hours (or 5/2 hours), we add this time to see how long Mr. Johnson is traveling when James starts.
Step 2: Determine Catch-Up Time
To find out how long it will take for James to catch Mr. Johnson, we calculate the total time. Mr. Johnson has traveled for 5 hours (the time before James starts chasing) plus his delayed time of 2.5 hours, resulting in a total of 7.5 hours. Now we can determine the total distance he covers during this time.
Step 3: Calculate James’ Required Speed
Finally, we determine the speed James needs to reach his father. Mr. Johnson covers 180 miles (from the total 24 miles/hour for 7.5 hours). James needs to cover this distance in 5 hours. To find the speed, we divide the distance by the time: 180 miles / 5 hours = 36 miles per hour. Hence, James must travel at 36 miles per hour to catch his father in time.