Question

Christy drove 300 miles on her vacation. She drove an average of 1.25 times faster on the second 150 miles of her trip. Which expression represents the time she spent driving? Let x= her speed on the first half of the trip.
a.375/x
b. 337.5/x
c.270x
d. 270/x

Answer 1

Correct answer is D.

During the first 150 miles, she drove 150 miles at a speed of x miles per hour, so her time was
$150 \text{ miles} = x * t_{1st}$ 
where $t_{1st}$ is the time she spent driving the first 150 miles.

On the second half of the trip, she drove at 1.25x miles per hour. There, the equation would be
$150 \text{ miles} = 1.25x * t_{2nd}$
where $t_{2nd}$ is the time she spent driving the second 150 miles.
 
Solve both of those equations for the t variables, then add them together. Your answer will be 
$t_{1st} + t_{2nd}= \frac{150}{x} + \frac{150}{1.25x}= \frac{150}{x} + \frac{120}{x}= \frac{270}{x}$