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 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

A- 375/x
B- 337.5/x
C- 270x
D- 270/x

Answer 1

Answer: Option 'D' is correct.

Explanation:

Since we have given that

Total miles she drove = 300 miles .

Let the speed on the first half of the trip be 'x'.

According to question, we have mention that she drove an average of 1.25 times faster on the second 150 miles of her trip than she did on the first 150 miles of her trip.

So, time taken in her first 150 miles would be

`(150)/(x)`

Time taken in her next 150 miles would be

`(150)/(1.25x)\\\\\\=\frac{120}x}`

Total time taken she spent on driving is given by

`(150)/(x)+(120)/(x)\\\\=(270)/(x)`

Hence, Option 'D' is correct.

Answer 2

This is the concept of algebra, we are required to calculate the time traveled by Christy in her trip, here we shall proceed as follows;
the speed traveled in the first trip= x mph
time=distance/speed
time taken in her first distance of the trip will be:
time=150/x

given that she traveled 1.25 times on her way back than when she was going, the speed she used on her way back will be 1.25x;
thus the time taken to travel back will be:
time=150/1.25x=120/x
thus the total traveling time was:
150/x+120/x
=270/x hours

the answer is D- 270/x