Help please, check my answer- not sure if my math it is right?

Question

jim and al wanted to drive all day. the first part on the highway they averaged 60 mph. they got to Houston and traffic made them average 30mph. the distance they drove in huston was 100 miles less than their distance on the highway. So what was their total driving distance if they spent 50 min more on the highway than they did in Houston?
I got the total miles as 100 miles. is this right? I don't think so please help me!!

Answer 1

d=r*t
highway= 60*highwaytime
city = 30*citytime
city = highway - 100
citytime =highway time - 5/6 50 min = 5/6 hour.
sub in

highway - 100 = 30 (highwaytime- 5/6)
60 * highwaytime - 100 = 30 * highwaytime - 30*5/6
simplify
30* highwaytime = 75
highwaytime = 2 1/2 hours
h =2.5*60 = 150 miles
city =30* 1 2/3 = 50 miles
total 200 miles

Answer 2

Rate on freeway = 60mph
Time on freeway = t + 5/6 (50 minutes minutes more than city)
Distance on freeway = d + 100

Rate on city streets = 30mph
Time on city streets = t
Distance on city streets = d

Two equations, two unknowns:
d = 30t
d + 100 = 60(t + 5/6)

Substitute d into the second equation:
30t + 100 = 60t +50
30t = 50
t = 5/3
t = 1 2/3 hours = 1 hr. 40 minutes


d = 30= 30(5/3) = 50 miles

On the freeway, distance was 100 more than this:
d = 150 miles.

So all together they drove *200* miles, not 100 miles.

Summarizing:
They drove on the freeway for 2 1/2 hours (2 hrs. 30 minutes) at 60 mph. They went 150 miles.
They drove on the city streets for 1 2/3 hours (1 hr 40 minutes) at 30 mph. They went 50 miles.

Adding together they went 200 miles.

Answer 3

Total distance is 200 miles. 150 on the highway @ 60mph takes 150 minutes. 50 in the city @ 30 mph takes 100 minutes.