Answer:
Time taken by Duke on the highway = 3 hours
Time spent on the construction = 6 hours
Time spent in the city = 2 hours
Step-by-step explanation:
Speed by which Duke travels a distance on highway  = 60 mph
 = 60 mph
Let the time taken to travel on highway =  hours
 hours
Distance traveled =  miles
 miles
Speed in the city = 40 mph
Let the time taken =  hours
 hours
Distance traveled in the city =  miles
 miles
Speed on the construction = 20 mph
Let the time spend on the construction =  hours
 hours
Distance traveled on the construction =  miles
 miles
Since, total distance covered = 380 miles

He spends one half the time on the highway as he does on the construction,

Total time spent in the trip = 11 hours
Therefore, 


From equation (1),




 
 
 hours
 hours
 hours
 hours
 hours
 hours
Therefore, time taken by Duke on the highway = 3 hours
Time spent on the construction = 6 hours
Time spent in the city = 2 hours