The total duration of the trip is 5 3/4 hours. Thus, you just need to calculate each segment separately.
Since you know he drove 168 miles in 3 1/2 hours, you only need to calculate how far he travelled for 2 1/4 hours.
Speed is distance per unit time.
Calculate 168 / 3.5h which will give you 48 miles per hour. That is the speed at first.
After that, the speed increases by 5miles per hour so it becomes 53 miles per hour.
calculate the distance (s × t) = 53 × 2 1/4
Add the two distances together which gives you 168 + (53 × 2 1/4) = 287.25 miles.