Question

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph through cities, he can only go 20 mph past the construction. He spends one half the time on the highway as he does in construction, so the 380-mile trip takes 11 hours. How much of this time does he spend on the highway, in the city, and through road construction?

Answer 1

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Explanation:

Speed by which Duke travels a distance on highway
`d_1` = 60 mph

Let the time taken to travel on highway =
`t_1` hours

Distance traveled =
`60t_1` miles

Speed in the city = 40 mph

Let the time taken =
`t_2` hours

Distance traveled in the city =
`40t_2` miles

Speed on the construction = 20 mph

Let the time spend on the construction =
`t_3` hours

Distance traveled on the construction =
`20t_3` miles

Since, total distance covered = 380 miles

`d_1+d_2+d_3=60t_1+40t_2+20t_3`

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

`t_3=2t_1`

Total time spent in the trip = 11 hours

Therefore,
`t_1+t_2+t_3=11`

`t_1+t_2+2t_1=11`

`t_2=11-3t_1`

From equation (1),

`60t_1+40(11-3t_1)+20(2t_1)=380`

`60t_1-120t_1+40t_1+440=380`

`440-20t_1=380`

`20t_1=440-380`

`t_1=(60)/(20)`

`t_1=3` hours

`t_2=11-3t_1=2` hours

`t_3=2t_1=6` 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