Author 
Message 
TAGS:

Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4476

Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
09 Jan 2015, 15:44
Question Stats:
64% (03:10) correct 36% (03:15) wrong based on 202 sessions
HideShow timer Statistics
Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mphFor a discussion of Motion questions on the GMAT, with five practice problems, including the OE of this particular question, see: http://magoosh.com/gmat/2014/gmatpract ... onmotion/Mike
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Mike McGarry Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1723
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
14 Jan 2015, 01:11
Refer diagram below: Attachment:
dist.png [ 8.78 KiB  Viewed 10866 times ]
At 01:30PM, both A & B are at the same position heading toward town Y. Let the distance from this point to Town Y = x Let speed of B = s, then speed of A = 1.25s At 03:15PM, A has reached destination, B is lagging behind by 35 miles It means time required by A for journey "x" distance = time required by B for journey "x35" distance. Setting up speed equation for A \(1.25s = \frac{x}{105}\) ............. (1) Setting up speed equation for B \(s = \frac{x35}{105}\) ............... (2) Divide (1) by (2) \(1.25 = \frac{x}{x35}\) x = 175 Speed of Car A\(= \frac{175}{105} * 60 = \frac{5}{3} * 60 = 100\) Answer = E




Senior Manager
Joined: 13 Jun 2013
Posts: 253

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
10 Jan 2015, 11:29
NOTE: When two cars travel in the same direction at different speed x, y (x>y). Then relative speed of faster Car with respect to slower car = xy. i.e. per hour the distance between faster and slower train will be increased at the rate of (xy).
Let's see, what happens after 1:30 pm. Car A, whose speed is 1.25 times the speed of car B will increase the distance between the two cars at the rate of (1.25BB) per hour = .25B.
so at 2:30 pm distance between car A and car B will be (.25B)*1 = .25B at 3:15 Car A has traveled for additional 45 minutes = 3/4 hr. hence the distance increased by car A in these 45 minutes = .25B(3/4)
so the total distance between A and B, when Car A reaches town Y = .25B+.25B(3/4) =\(\frac{7B}{16}\)
this distance between A and B is equal to 35 as per the question. hence we have \(\frac{7B}{16}\) = 35 or B= 80 so speed of A = 1.25(80) = 100



Manager
Joined: 22 Oct 2014
Posts: 85
Concentration: General Management, Sustainability
GPA: 3.8
WE: General Management (Consulting)

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
09 Jan 2015, 17:07
We know that within 1 hour 45 minutes, car A drives 35 miles more than car B. Therefore:
\(\frac{7}{4}* \frac{1}{4}x=35\)
where 7/4 is 1 hour 45 minutes, 1/4*x is the relative speed of car A to car B and x is the speed of car B.
We solve for x and get 80. Since car A is driving at 1.25 the speed of car B, the speed of car A is 100. Answer E.



Manager
Joined: 18 Jan 2010
Posts: 238

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
13 Jun 2016, 23:03
mikemcgarry wrote: Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mphFor a discussion of Motion questions on the GMAT, with five practice problems, including the OE of this particular question, see: http://magoosh.com/gmat/2014/gmatpract ... onmotion/Mike Let speed of B: s. Then speed of A:1.25s Car A and B are together at 1:30 PM. Car A reaches Town Y at 3:15 PM. so A takes (1hour 45 minutes) to reach town Y (This is the time taken after A meets B) Distance travelled by A: (1hour 45 minutes) * 1.25s Now in this 1hour 45 minutes, Y is travelling with a speed s. It covers a distance D = (1hour 45 minutes) * sEquation: D+35 = (1hour 45 minutes) * 1.25s1hour 45 minutes = 1.75 hours. 1.75s +35 = 1.75 * 1.25ss works out to 80. Speed of A = 1.25 *80 = 100 mph. E is the answer.



Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 482

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
03 Feb 2018, 08:57
In 1 hour 45 minutes, car A drives 35 miles more than car B. For relative speed of bodies moving in same direction, the equation is (Sx  Sy) X t = Distance1 hour 45 minutes = \(\frac{7}{4}\) hour Relative speed = \(1.25xx=0.25x=\frac{1}{4} x\) \(\frac{1}{4} x*\frac{7}{4}=35\) \(x=80\) \(∴1.25x=100\)
_________________



Intern
Joined: 10 Aug 2015
Posts: 30
Location: India
GPA: 3.5
WE: Consulting (Computer Software)

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
05 Sep 2016, 02:39
mikemcgarry wrote: Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mphFor a discussion of Motion questions on the GMAT, with five practice problems, including the OE of this particular question, see: http://magoosh.com/gmat/2014/gmatpract ... onmotion/Mike This question becomes very simple if you think in terms of distance. According to stem at 1.30PM they were at same place but at 3.15PM(105mins or 7/4hour) car A was 35 miles ahead. So difference in their speed = 35/(7/4)= 5*4= 20 miles/hour. Now we know A's time is 25% less than B's time. due to inverse proportionality we know A' speed was 25% more than B's.
So our eqn becomes Speed of ASpeed of B= 1.25BB=.25B=20. Speed of B = 80. But don't fall for trap answer now as stem asks Speed of A which is 25% more. So answer is 100 miles/hr.



Intern
Joined: 09 Apr 2013
Posts: 31

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
12 Jan 2015, 12:03
let speed of B = x mph Therefore speed of A = 1.25x mph
By the time A reaches Destination, B is 35 miles behind the destination. and time taken by A to keep a 35 miles gap with B is time between 1:30 pm and 3:15 pm => 1.75 hrs
therefore => 35/(speed of A  speed of B) = 1.75 35/(0.25x) = 1.75
on solving for x => 80 i.e speed of B
Speed of A = 80*1.25 = 100
hence E



VP
Joined: 07 Dec 2014
Posts: 1230

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
05 Sep 2016, 13:32
Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mph
let d=distance from passing to Town Y d/(d35)=5/4 d=175 miles 175 miles/1.75 hrs=100 mph A's speed is 100 mph



Senior Manager
Joined: 15 Jan 2017
Posts: 324

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
04 Sep 2017, 08:59
adiagr wrote: mikemcgarry wrote: Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mphFor a discussion of Motion questions on the GMAT, with five practice problems, including the OE of this particular question, see: http://magoosh.com/gmat/2014/gmatpract ... onmotion/Mike Let speed of B: s. Then speed of A:1.25s Car A and B are together at 1:30 PM. Car A reaches Town Y at 3:15 PM. so A takes (1hour 45 minutes) to reach town Y (This is the time taken after A meets B) Distance travelled by A: (1hour 45 minutes) * 1.25s Now in this 1hour 45 minutes, Y is travelling with a speed s. It covers a distance D = (1hour 45 minutes) * sEquation: D+35 = (1hour 45 minutes) * 1.25s1hour 45 minutes = 1.75 hours. 1.75s +35 = 1.75 * 1.25ss works out to 80. Speed of A = 1.25 *80 = 100 mph. E is the answer. hi! thank you for this answer . Why do we put D+35 while equating? Why not just 35?



Intern
Joined: 04 Sep 2017
Posts: 4

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
04 Sep 2017, 09:10
Very helpful. Thanks
_________________
 When The Going Gets Tough  https://www.essayagents.com Home of high quality research papers, essays, and dissertations.



Intern
Joined: 21 Sep 2016
Posts: 28

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
12 Sep 2017, 17:01
Let A be the average speed of car A, thus B will be the same for said vehicle.
We know, according to the question, that A = 1.25B
Also, we know that B lost 35 miles in 1h 45 min > 7/4 hours.
So, in order to know how many miles per hour does B lose to A: 34/(7/4) = 20.
We know now that car A is 20 mph faster, so:
\(A = B + 20\)
\(B+20 = 1.25B\)
B = 80 A = 1.25*80 = 100.



Director
Joined: 31 Jul 2017
Posts: 503
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
04 Feb 2018, 12:30
mikemcgarry wrote: Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mphFor a discussion of Motion questions on the GMAT, with five practice problems, including the OE of this particular question, see: http://magoosh.com/gmat/2014/gmatpract ... onmotion/Mike Let d be the distance from the first meeting point to point Y.\(Va = 1.25Vb\) \(d = Va * t\) \(d  35 = Vb * t\) \(d = 175\). Given, the time taken by A from first meeting point to Point Y = \frac{7}{4} Hours \(175 = Va*\frac{7}{4}\) \(Va = 100mph\)



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9142
Location: United States (CA)

Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
Show Tags
07 Apr 2019, 18:42
mikemcgarry wrote: Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A? (A) 60 mph (B) 75 mph (C) 80 mph (D) 96 mph (E) 100 mph From 1:30 pm to 3:15 pm, the time elapsed is 1 hour 45 minutes, or 1.75 hours. We see that during this time, Car A travels 35 miles more than Car B since its speed is 1.25 times that of Car B. Therefore, if we let r = speed of Car B, we can create the equation: . (1.25r)(1.75) = 1.75r + 35 1.25(1.75r) = 1.75r + 35 1.25(1.75r)  1.75r = 35 0.25(1.75r) = 35 1.75r = 140 r = 140/1.75 = 140/(7/4) = (4 x 140)/7 = 4 x 20 = 80 Since Car A’s speed is 1.25 times the speed of Car B, Car A’s speed is 1.25 x 80 = 100 mph. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: Cars A and B are traveling from Town X to Town Y on the same route at
[#permalink]
07 Apr 2019, 18:42






