Since they are moving in the opposite direction (towards each other), their relative speed \(= 50 + 70 = 120mph\)

Time required to meet \(= \frac{190}{120} = 1.5833hours\) i.e. \(1\) hour \(35\) minutes

So \(45\) minutes before means, they travelled for \(50\) minutes

In \(50\) minutes, Rachel covered \(= (50)\frac{50}{60} = 41.667miles\) and Rob covered \(= (70)\frac{50}{60} = 58.333miles\)

Distance between them \(= 190 - 41.667 - 58.333 = 90miles\)

Hence, option D

Rachel ---------A ___________ B---------------Rob

As they drive in opposite direction, at 45min = 0.75hr before meeting, let's say that Rachel is at point A and Rob is at point B.
We know that they both meet after 45 mins which basically means that they both travelled distance AB in that last 45 mins.
So, AB = 50*0.75 + 70*0.75 = 90 miles

distance, rate, time
190, 50+70=120mph, time
190, 120/60=2mpm, 95min
90, 2mpm, 45min

Simply 2 miles per minute x 45 minutes (distance to be covered) = 90

I found my problem, I missed the word "before",

Hey everybody,
Why my approach provides a different answer?

Rachel - Speed: 50
Rob - Speed: 70

Total Speed: 120

They drove toward each other for 45 minutes (3/4 hours).

120x(3/4) = 90

They passed 90 miles together and the total distance was 190.
Therefore, they must still drive 100 miles to meet each other (190 - 90).
So the distance between them after 45 minutes is 100 miles.

Why doesn't my approach work?

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.