Last visit was: 13 Dec 2024, 10:41 It is currently 13 Dec 2024, 10:41
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
meprarth
avatar
Joined: 12 Jan 2011
Last visit: 05 Jun 2012
Posts: 17
Own Kudos:
43
 []
Given Kudos: 35
Status:Life.. Be Kind to me
Location: India
Schools: Tuck '14 ISB HKUST
WE:Engineering (Telecommunications)
Schools: Tuck '14 ISB HKUST
Posts: 17
Kudos: 43
 []
A taxi leaves Point A 5 hours after a bus left the same spot Updated on: 27 Mar 2013, 05:38
Originally posted by meprarth on 18 Apr 2011, 05:45.
Last edited by Bunuel on 27 Mar 2013, 05:38, edited 1 time in total.
Renamed the topic and edited the question.
5
Kudos
Add Kudos
31
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

79% (02:17) correct 21% (02:29) wrong based on 711 sessions

History

Date
Time
Result
Not Attempted Yet
A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

(A) 44
(B) 46
(C) 48
(D) 50
(E) 52
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
gmat1220
User avatar
Joined: 03 Feb 2011
Last visit: 17 Feb 2020
Posts: 467
Own Kudos:
925
 []
Given Kudos: 123
Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Products:
My Reviews
Posts: 467
Kudos: 925
 []
A taxi leaves Point A 5 hours after a bus left the same spot 18 Apr 2011, 07:03
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Let the speed of bus be v - 30, speed of taxi be v

The bus travelled a total of 8 hrs and taxi a total of 3 hrs.

Hence 8 * (v-30) = 3v
8v - 240 = 3v
5v = 240
v = 48 mph

PS : I referred GMATPill SC Guide this morning and got some wrong OA and some debatable OA. I think this probability extends even to the Quant section of the guide where some OA may be wrong. I will advise you to contact the author and inform the discrepancy.
General Discussion
User avatar
subhashghosh
User avatar
Retired Moderator
Joined: 16 Nov 2010
Last visit: 25 Jun 2024
Posts: 903
Own Kudos:
1,219
 []
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Products:
My Reviews
Posts: 903
Kudos: 1,219
 []
A taxi leaves Point A 5 hours after a bus left the same spot 18 Apr 2011, 07:31
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I'm also getting 48 by both methods :

Speed of taxi = x

Speed of bus = x - 30

5(x-30) + 3 (x-30) = 3x

8x - 240 = 3x

5x = 240
x = 48

Relative Speed method :

5(x-30)/30 = 3

x = 18 + 30 = 48
User avatar
Spidy001
User avatar
Joined: 01 Feb 2011
Last visit: 16 Feb 2015
Posts: 302
Own Kudos:
334
Given Kudos: 42
Posts: 302
Kudos: 334
A taxi leaves Point A 5 hours after a bus left the same spot 18 Apr 2011, 08:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let v be the speed of the taxi

3v = (v-30)8

=> v = 48 mph

Posted from my mobile device
User avatar
GMATPill
User avatar
Joined: 14 Apr 2009
Last visit: 17 Sep 2020
Posts: 2,261
Own Kudos:
3,727
 []
Given Kudos: 8
Location: New York, NY
Posts: 2,261
Kudos: 3,727
 []
A taxi leaves Point A 5 hours after a bus left the same spot 26 Mar 2013, 22:35
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
subhashghosh
I'm also getting 48 by both methods :

Speed of taxi = x

Speed of bus = x - 30

5(x-30) + 3 (x-30) = 3x

8x - 240 = 3x

5x = 240
x = 48

Relative Speed method :

5(x-30)/30 = 3

x = 18 + 30 = 48


Yes it's 48.

A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 30 mph
slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

(A) 44

(B) 46

(C) 48

(D) 50

(E) 52


The idea in this question is to set the distance for each of them to be equivalent. Each of them has a distinct "r*t". Set these equal to each other because the distance covered for each will be the same at the moment that the taxi overcomes the bus.
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,328
Own Kudos:
2,571
 []
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,328
Kudos: 2,571
 []
A taxi leaves Point A 5 hours after a bus left the same spot 31 Dec 2013, 09:56
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
meprarth
A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

(A) 44
(B) 46
(C) 48
(D) 50
(E) 52

(T-B)(3) = 5B

and B= T-30

Hence, T =48

Answer is C

Gimme some Kudos will ya?

Cheers!
J :)
User avatar
gracie
User avatar
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,048
Own Kudos:
1,715
 []
Given Kudos: 27
Posts: 1,048
Kudos: 1,715
 []
A taxi leaves Point A 5 hours after a bus left the same spot 30 Sep 2015, 15:19
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why is the bus only doing 18 mph? Is it some kind of special GMAT bus?
User avatar
TeamGMATIFY
User avatar
Joined: 20 Aug 2015
Last visit: 31 Oct 2016
Posts: 346
Own Kudos:
1,438
 []
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Expert reply
GMAT 1: 760 Q50 V44
Posts: 346
Kudos: 1,438
 []
A taxi leaves Point A 5 hours after a bus left the same spot 01 Oct 2015, 04:29
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gracie
Why is the bus only doing 18 mph? Is it some kind of special GMAT bus?
That is an interesting question. May be it is a sign that you should not board this bus :)

As for solving the question.

Let us assume that the speed of the Taxi = x
Hence the speed of the bus = x - 30

At the point of overtaking, both the bus and the taxi would have covered equal distance, so we can safely equate them
Also, note that the Taxi has been running for 3 hours, whereas the bus has been running for 8 hours.

\(x*3 = (x-30)*8\)
\(3x = 8x - 240\)
\(5x = 240\)
Or \(x = 48\). Option C
User avatar
Skywalker18
User avatar
Retired Moderator
Joined: 08 Dec 2013
Last visit: 15 Nov 2023
Posts: 2,079
Own Kudos:
9,308
Given Kudos: 171
Status:Greatness begins beyond your comfort zone
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Products:
My Reviews
Posts: 2,079
Kudos: 9,308
A taxi leaves Point A 5 hours after a bus left the same spot 02 Oct 2015, 11:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let Speed of Bus =Sb
and Speed of Taxi =St

St = Sb + 30

Distance travelled by Bus in 8 hours is same as the distance travelled by taxi in 3 hours

8 Sb = 3 St
=> 8 Sb = 3Sb + 90
=> Sb= 18

St=48 :-D
User avatar
hanyhamdani
User avatar
Current Student
Joined: 30 Dec 2013
Last visit: 04 Jan 2019
Posts: 28
Own Kudos:
27
Given Kudos: 26
Status:preparing
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
Schools: Tepper '19 Kenan-Flagler '19 Darden '19 Duke '19 Tuck '19 Stern '19 McCombs '19 Carlson '19 Foster '20 Schulich Sept 18 Intake (A)
GMAT 1: 660 Q45 V35
GMAT 2: 640 Q49 V28
GPA: 2.84
WE:General Management (Consumer Packaged Goods)
Schools: Tepper '19 Kenan-Flagler '19 Darden '19 Duke '19 Tuck '19 Stern '19 McCombs '19 Carlson '19 Foster '20 Schulich Sept 18 Intake (A)
GMAT 2: 640 Q49 V28
Posts: 28
Kudos: 27
A taxi leaves Point A 5 hours after a bus left the same spot 18 Nov 2016, 09:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let Vt be speed of taxi.
therefore bus speed is : Vb=Vt-30

Since bus left point A, 5 hours before the taxi left. so the distance travelled by bus will be
d=5(Vt-30)=5Vt-150 ........(a)
GIven that, taxi overtakes the bus after 3 hours. So,
t=d/ (relative speed) where relative speed is (Vt-Vb)= Vt-(Vt-30)=30

3= (5Vt-150) / 30
90+150= 5Vt
Vt=48

Answer is C
avatar
rounakkedia172
avatar
Joined: 13 Jul 2018
Last visit: 20 Sep 2022
Posts: 36
Own Kudos:
15
Given Kudos: 163
GMAT 1: 660 Q46 V35
GMAT 1: 660 Q46 V35
Posts: 36
Kudos: 15
A taxi leaves Point A 5 hours after a bus left the same spot 20 Jun 2020, 01:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
meprarth
A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

(A) 44
(B) 46
(C) 48
(D) 50
(E) 52

Experts please help TeamGMATIFY GMATPill Bunuel

I solved it in an interesting way, I am not sure if it is right or wrong.

Relative speed = 30km/hr
Relative distance covered in 3 hours by the car = 30*3 = 90 kms
this 90 kms were what the bus drove in that 5 hours headstart.

Speed of the bus = 90/5 = 18km/hr
Speed of the car = 18+30 = 48km/hr
avatar
EffioCreo
avatar
Joined: 07 Jan 2021
Last visit: 02 Oct 2021
Posts: 2
Own Kudos:
1
Given Kudos: 10
Posts: 2
Kudos: 1
A taxi leaves Point A 5 hours after a bus left the same spot 10 Jan 2021, 22:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(5+3)(x-30)= 3x
8(x-30)= 3x
8x-240=3x
8x-240-3x=0
5x-240=0
x=240/5
x= 48

Posted from my mobile device
User avatar
BelisariusTirto
User avatar
Joined: 03 Oct 2024
Last visit: 13 Dec 2024
Posts: 9
Own Kudos:
1
Given Kudos: 14
Posts: 9
Kudos: 1
A taxi leaves Point A 5 hours after a bus left the same spot 23 Nov 2024, 20:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sorry to revive an old thread but for the second method why do we divide by 30? Thank you.
subhashghosh
I'm also getting 48 by both methods :

Speed of taxi = x

Speed of bus = x - 30

5(x-30) + 3 (x-30) = 3x

8x - 240 = 3x

5x = 240
x = 48

Relative Speed method :

5(x-30)/30 = 3

x = 18 + 30 = 48
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Dec 2024
Posts: 97,873
Own Kudos:
685,588
Given Kudos: 88,268
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,873
Kudos: 685,588
A taxi leaves Point A 5 hours after a bus left the same spot 24 Nov 2024, 01:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BelisariusTirto
Sorry to revive an old thread but for the second method why do we divide by 30? Thank you.
subhashghosh
A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

(A) 44
(B) 46
(C) 48
(D) 50
(E) 52

I'm also getting 48 by both methods :

Speed of taxi = x

Speed of bus = x - 30

5(x-30) + 3 (x-30) = 3x

8x - 240 = 3x

5x = 240
x = 48

Relative Speed method :

5(x-30)/30 = 3

x = 18 + 30 = 48

In that method, we divide the distance between the bus and the taxi, 5(x - 30) miles, by the relative speed of the bus and the taxi, which is x - (x - 30) = 30 mph. This gives the time it takes for the taxi to catch up to the bus, which is 3 hours.

Hope it's clear.
Moderator:
Bunuel
Math Expert
97873 posts