Katalin drove 180 miles on her vacation. She drove an average of 1.5 times faster on the second 90 miles of her trip than she did on the first 90 miles of her trip. Which expression represents the time she spent driving? Let x = her speed on the first half of the trip.
Since time = distance/speed, the time spent driving on the first 90 miles is 90/x.
The speed on the second 90 miles is 1.5x.
Thus, the time spent driving on the second 90 miles is 90/(1.5x) = 60/x.
The total time spent driving is the sum of the time spent driving on the first and second 90 miles, or 90/x + 60/x.