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.