Question

Debora drove 400 miles on her vacation. She drove an average of 1.5 times faster in the second 200 miles of her trip than she did on the first 200 miles of her trip. Which expression represent the time she spent driving? Let x = her speed on the first half of her trip.

Answer 1

$t=\dfrac{s}{v}$
Time, she spent driving the first 200 miles:
$\dfrac{200}{x}$
Time, she spent driving the second 200 miles:
$\dfrac{200}{1.5\cdot x}$

Total time:
$\dfrac{200}{x}+\dfrac{200}{1.5\cdot x}=\dfrac{200}{x}\cdot \dfrac{1.5}{1.5}+\dfrac{200}{1.5\cdot x}=\dfrac{300}{1.5\cdot x}+\dfrac{200}{1.5\cdot x}=\dfrac{500}{1.5\cdot x}=\boxed{\dfrac{1000}{3\cdot x}}$