Last visit was: 20 Jul 2024, 09:50 It is currently 20 Jul 2024, 09:50
Toolkit
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

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.

# A taxi leaves Point A 5 hours after a bus left the same spot

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 12 Jan 2011
Status:Life.. Be Kind to me
Posts: 18
Own Kudos [?]: 39 [33]
Given Kudos: 35
Location: India
Schools: Tuck '14 ISB HKUST
WE:Engineering (Telecommunications)
Senior Manager
Joined: 03 Feb 2011
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
Posts: 469
Own Kudos [?]: 904 [5]
Given Kudos: 123
General Discussion
Intern
Joined: 12 Jan 2011
Status:Life.. Be Kind to me
Posts: 18
Own Kudos [?]: 39 [0]
Given Kudos: 35
Location: India
Schools: Tuck '14 ISB HKUST
WE:Engineering (Telecommunications)
Retired Moderator
Joined: 16 Nov 2010
Posts: 903
Own Kudos [?]: 1194 [2]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
2
Kudos
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
Manager
Joined: 26 Jul 2010
Posts: 56
Own Kudos [?]: 67 [0]
Given Kudos: 6
Location: India
Concentration: Operations, General Management
Schools: IIMA (M)
GMAT 1: 640 Q48 V29
GMAT 2: 670 Q49 V31
WE:Supply Chain Management (Military & Defense)
Senior Manager
Joined: 01 Feb 2011
Posts: 306
Own Kudos [?]: 328 [0]
Given Kudos: 42
Let v be the speed of the taxi

3v = (v-30)8

=> v = 48 mph

Posted from my mobile device
SVP
Joined: 14 Apr 2009
Posts: 2261
Own Kudos [?]: 3701 [1]
Given Kudos: 8
Location: New York, NY
1
Bookmarks
subhashghosh wrote:
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. The link to the original question is here:

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.
VP
Joined: 06 Sep 2013
Posts: 1335
Own Kudos [?]: 2446 [4]
Given Kudos: 355
Concentration: Finance
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
3
Kudos
1
Bookmarks
meprarth wrote:
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

Gimme some Kudos will ya?

Cheers!
J
VP
Joined: 07 Dec 2014
Posts: 1067
Own Kudos [?]: 1608 [2]
Given Kudos: 27
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
2
Kudos
Why is the bus only doing 18 mph? Is it some kind of special GMAT bus?
Tutor
Joined: 20 Aug 2015
Posts: 349
Own Kudos [?]: 1409 [3]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
3
Kudos
gracie wrote:
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
Retired Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2093
Own Kudos [?]: 8987 [0]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
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
Current Student
Joined: 30 Dec 2013
Status:preparing
Posts: 28
Own Kudos [?]: 26 [0]
Given Kudos: 26
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35
GMAT 2: 640 Q49 V28
GPA: 2.84
WE:General Management (Consumer Products)
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
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

Intern
Joined: 13 Jul 2018
Posts: 37
Own Kudos [?]: 14 [0]
Given Kudos: 163
GMAT 1: 660 Q46 V35
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
meprarth wrote:
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 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
Intern
Joined: 07 Jan 2021
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 10
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
(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
Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
Moderator:
Math Expert
94430 posts