Katalin drove 300 miles on her vacation. She drove an average of 1.9 times faster on the second 150 miles of her trip than she did on the first 150 miles of her trip. Which expression represents the time she spent driving? Let x = her speed on the first half of the trip.
228.95/x
228.95x
457.89/x
435/x
Let's say that Katalin drove at a speed of x miles per hour on the first 150 miles of her trip.
Therefore, the time she spent driving on the first 150 miles is 150/x hours.
On the second 150 miles of her trip, she drove 1.9 times faster, which means she drove at a speed of 1.9x miles per hour.
Therefore, the time she spent driving on the second 150 miles is 150/1.9x hours.
The total time she spent driving on her vacation is the sum of the time spent driving on the first and second halves.
Total time = 150/x + 150/1.9x
To find a simplified expression for the total time, we can multiply both fractions by the lowest common multiple of the denominators, which is 1.9x.
Total time = 150(1.9x)/(x)(1.9x) + 150(x)/(x)(1.9x)
Total time = (285x + 150x)/(1.9x)(x)
Total time = 435x/(1.9x)(x)
Total time = 435/(1.9x)
Therefore, the expression that represents the time she spent driving is 435/(1.9x), which is equivalent to 228.95/x when simplified.
So the correct expression is 228.95/x.