• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Speed Time Distance MGMAT

This topic has 4 expert replies and 1 member reply

Speed Time Distance MGMAT

Post
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?

(1) Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Quote:
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?

(1) Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.
Let A = A's rate and B = Brian's rate.

Ashok has to CATCH-UP by 30 miles.
The CATCH-UP rate is equal to the DIFFERENCE between the two rates.
If A = 3mph, while B = 2mph, then every hour A walks 1 more mile than B, with the result that every hour A catches up by 1 mile -- the DIFFERENCE between the two rates:
A-B = 3-2 = 1mph.

Statement 1: Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.
Thus:
B = 2(A-B)
B = 2A - 2B
3B = 2A
A = (3/2)B.

Case 1: B = 10mph, A = (3/2)(10) = 15mph
Here, the catch-up rate = A-B = 15-10 = 5mph.
Time for A to catch up by 30 miles = (catch-up distance)/(catch-up rate) = 30/5 = 6 hours.
In 6 hours, the distance traveled by B at a rate of 10mph = r*t = 10*6 = 60 miles.

Case 2: B = 20mph, A = (3/2)(20) = 30mph
Here, the catch-up rate = A-B = 30-20 = 10mph.
Time for A to catch up by 30 miles = (catch-up distance)/(catch-up rate) = 30/10 = 3 hours.
In 3 hours, the distance traveled by B at a rate of 20mph = r*t = 20*3 = 60 miles.

Since B travels the SAME DISTANCE in each case, SUFFICIENT.

Statement 2: If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

Thus:
5A = 3(A+B)
5A = 3A + 3B
2A = 3B
A = (3/2)B.
Same information as statement 1.
SUFFICIENT.

The correct answer is D.

_________________
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.
Master | Next Rank: 500 Posts Default Avatar
Joined
04 Jul 2010
Posted:
418 messages
Followed by:
2 members
Upvotes:
6
Post
Since both A and B started at the same time, they both spent same time, t.
Let d be the extra distance B traveled beyond 30m.

Time spent by Ashok = Time spent by Brian

Time spent by Ashok = distance traveled / speed =
Let Speed of Ashok = a meters; distance = 30 + d
Time spent by Ashok = (30+d)/a..............(1)

Time spent by Brian = distance Brian traveled / speed of Brian
Speed of Brian = b; distance traveled by Brian = d meters
Time spent by Brian = d/b...................(2)

Equating (1) to (2), we have
(30+d)/a = d/b
30b + bd = ad
a/b = d/(30+d)...if we know the ratio of their speed(a/b) that would be sufficient
to find d.

Both statements can be reduced to give a ratio of a/b.. D.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor Default Avatar
Joined
12 Sep 2012
Posted:
2636 messages
Followed by:
114 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post
We can use our standard Distance = Rate * Time equation here, but we have to be careful about how we define each of the terms.

Let's say that Brian's rate is b, and the distance he travels is d. We'll say that Ashok's rate is a, and since he has to travel 30 miles further than Brian does, Ashok's distance is (d + 30).

Since they start walking at the same time and meet each other at the same time, their times are the same, so let's call each guy's time t.

This gives us the equations

d = bt
d + 30 = at

which reduces to bt = at - 30. We want to solve for bt, since bt = Brian's Rate * Brian's Time = Brian's Distance.

S1 tells us that b = 2*(a - b), or 3b = 2a, or a = (3/2)b. Subbing this into our equation above gives us

bt = (3/2)bt - 30, or
30 = (1/2)bt, or
60 = bt

So b*t = 60, and we're done!

S2 gives us 5a = 3(a + b), or 2a = 3b, which is the same as what we got in S1, making this statement ALSO sufficient.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post
rommysingh wrote:
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?
(1) Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.
(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.
GIVEN: When the men start walking, Brian has a 30-mile lead

Let B = Brian's walking speed (in miles per hour)
Let A = Ashok's walking speed (in miles per hour)

Since Ashok's speed is greater than Brian's speed, the rate at which the gap shrinks = (A - B) miles per hour
For example, if A = 5 and B = 2, then the 30-mile gap will shrink at a rate of (5 - 2) mph.

time = distance/speed

So, time for 30-mile gap to shrink to zero = 30/(A - B)

Target question: How many miles will Brian walk before Ashok catches up with him?
This is a good candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

distance = (speed)(time)
So, the distance Brian travels = (B)(30/(A - B))
Simplify to get: 30B/(A - B)

REPHRASED target question: What is the value of 30B/(A - B)?

Statement 1: Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.
We can write: B = 2(A - B)
Expand: B = 2A - 2B
This means: 3B = 2A
So: 3B/2 = A
Or we can say: 1.5B = A

Now take 30B/(A - B) and replace A with 1.5B to get: 30B/(1.5B - B)
Simplify: 30B/(0.5B)
Simplify: 30/0.5
Evaluate 60 (miles)
Perfect!! The answer to the REPHRASED target question is Brian will travel 60 miles
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT


Statement 2: If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.
We can write: 5A = 3(A + B)
Expand: 5A = 3A + 3B
Rewrite as: 2A = 3B
We get: A = 3B/2 = 1.5B
At this point, we're at the same place we got to for statement 1.
So, since statement 1 is sufficient, we know that statement 2 is also sufficient.


Answer: D

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
rommysingh wrote:
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?

(1) Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
This is a catching up problem. Recall that the time needed for the slower person (Brian) to catch up with the faster person (Ashok) is (difference in distances)/(difference in speeds). Here the difference in their distances is 30, and the difference in their speeds is (a - b), where a is Ashok’s speed and b is Brian’s speed. So the time for Brian to catch up with Ashok is 30/(a - b). If we can determine that, then we can determine the distance walked by Brian.

Statement One Alone:

Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

We are given that b = 2(a - b). That is,:

b = 2a - 2b

3b = 2a

a = 3b/2.

Therefore, the time for Brian to catch up with Ashok is 30/(a - b) = 30/(3b/2 - b) = 30/(b/2) = 60/b and the distance walked by Brian is b x 60/b = 60 miles. Statement one alone is sufficient.

Statement Two Alone:

If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

We are given that 5a = 3(a + b). That is:

5a = 3a + 3b

2a = 3b

a = 3b/2.

We can see that this statement provides the same information as statement one. So statement two is also sufficient.

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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

Top First Responders*

1 fskilnik@GMATH 89 first replies
2 Jay@ManhattanReview 50 first replies
3 Brent@GMATPrepNow 47 first replies
4 GMATGuruNY 30 first replies
5 Rich.C@EMPOWERgma... 22 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@GMATH

GMATH Teacher

181 posts
2 image description Scott@TargetTestPrep

Target Test Prep

150 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

111 posts
4 image description Max@Math Revolution

Math Revolution

91 posts
5 image description Jay@ManhattanReview

Manhattan Review

78 posts
See More Top Beat The GMAT Experts