BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Two motorists start a journey at opposite ends of the state

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Two motorists start a journey at opposite ends of the state

by BTGmoderatorLU » Fri Mar 02, 2018 5:00 am
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.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Mar 02, 2018 5:52 am
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Thu Mar 08, 2018 5:01 pm
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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Fri Mar 09, 2018 9:35 am
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!
Top
Post new topic Post Reply
• Page 1 of 1