• Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Two motorists start a journey at opposite ends of the state

This topic has 2 expert replies and 1 member reply

Two motorists start a journey at opposite ends of the state

Post
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
LUANDATO wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210
When A and B travel toward each other, they WORK TOGETHER to cover the 375 miles between them.

Motorist B travels at an average rate one-third slower than Motorist A travels.
If A's rate = 3 miles per hour, then B's rate = 3 - (1/3)3 = 3-1 = 2 miles per hour.
Implication:
Of every 5 miles traveled when A and B work together, A travels 3 miles, while B travels 2 miles.
Thus, A will travel 3/5 of the 375-mile distance:
(3/5)(375) = (3)(75) = 225 miles.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
LUANDATO wrote:
Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?

A. 275
B. 250
C. 225
D. 215
E. 210
Two motorists, A and B, starting a trip at opposite ends of a 375-mile road meet somewhere on that road. Thus, we know that the sum of the distances that their two cars have traveled will equal 375 miles. We can summarize this with the following equation:
distance of A + distance of B = total distance = 375

We are given that the rate of Motorist A is 375/5 = 75 mph and that the rate of Motorist B is 1/3 slower, or 2/3(75) = 50 mph. We can let the travel time of each motorist = t. Thus:

75t + 50t = 375

125t = 375

t = 3

Thus, Motorist A had driven 75 x 3 = 225 miles when he passed Motorist B’s car.

Answer: C

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag
Post
Hi LUANDATO,

Also, you can solve this question as follow,

Speed of A = 375/5 = 75 miles per hour.

Speed of B = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour.

Since they are moving in oppositive directions, their relative speed = (75 + 50) = 125 miles per hour.

The time taken to cover the distance = 275 / 125 = 3 hours.

In 3 hours, A covered = 3 * 75 = 225 miles. Option C.

Regards!

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 81 first replies
2 Brent@GMATPrepNow 71 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

202 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

163 posts
3 image description Scott@TargetTestPrep

Target Test Prep

118 posts
4 image description Jay@ManhattanReview

Manhattan Review

94 posts
5 image description Max@Math Revolution

Math Revolution

94 posts
See More Top Beat The GMAT Experts