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

Redeem

Speed Time Distance MGMAT

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 112
Joined: Thu Mar 22, 2012 9:33 am
Thanked: 1 times
Followed by:1 members

Speed Time Distance MGMAT

by rommysingh » Thu Sep 03, 2015 11:37 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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.
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 » Thu Sep 03, 2015 5:54 pm
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.
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
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Fri Sep 04, 2015 4:10 am
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.
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Sep 04, 2015 5:23 pm
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.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 06, 2018 6:15 am
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: https://www.gmatprepnow.com/module/gmat- ... cy?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
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

hi

by Scott@TargetTestPrep » Wed Nov 07, 2018 6:08 pm
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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1