Mr. johnson leaves on a trip planning to travel 24 mph. how fast must his son james travel to overtake him in 5 hours if he starts 2 1 2 hours after his father?

The distance traveled by Mr.Johnson in 1 hour = 24 miles
Time after which his son James starts the chase = 2 1/2 hours
                                                                                 = 5/2 hours
                                                                                 = 2.5 hours
Then
time after which James will catch Mr.Johnson = 5 + 2.5 hours
                                                                          = 7.5 hours
Distance traveled by Mr.Johnson in 7.5 hours = 24 * 7.5 miles
                                                                         = 180 miles
So the distance James need to cover is 180 miles and that has to be covered in 5 hours
So
Speed at which James needs to travel = 180/5 miles per hour
                                                               = 36 miles per hour
From the above deduction we can conclude that James needs to travel at a speed of 36 miles per hour to catch his fathe in 5 hours.