Yes, if he ran a total distance of 4 km in a total time of 1.75 hours then his average speed was 4/1.75= 2.29 km/h. That was the easy part!
Let v be the speed at which he runs the first 0.5 km in km/h. It takes him 0.5/v hours to run that part. He runs the remaining 3.5 km at twice that speed, 2v so that takes 3.5/(2v)= 1.75/v hours. Including the 90 minute= 1.5 hour nap, the total time was 0.5/v+ 1.75/v+ 1.5= 2.25/v+ 1.5= 1.75 h. From that 2.25/v= 1.75 1.5= 0.25. 2.25= 0.25v so v= 2.25/0.25= 9 km/h.
As a check, at 9 km/h it would take 0.5/9= 0.056 h to run the first 0.5 km. At twice that speed, 18 km/h, it would take 3.5/18= 0.194 h to run the remaining 3.5 km. Including the 1.5 h nap, that would be a total time of 0.056+ 0.194+ 1.5= 1.75 hours as required.
