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

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meprarth
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A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   Updated on: 27 Mar 2013, 05:38
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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
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C

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.
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gmat1220
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Re: Speed of bus [#permalink] New post   18 Apr 2011, 07:03
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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.
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Re: Speed of bus [#permalink] New post   18 Apr 2011, 07:17
Thanks! even i got 48 as the answer
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Re: Speed of bus [#permalink] New post   18 Apr 2011, 07:31
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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
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Re: Speed of bus [#permalink] New post   18 Apr 2011, 07:39
answer should be 48
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Re: Speed of bus [#permalink] New post   18 Apr 2011, 08:16
Let v be the speed of the taxi

3v = (v-30)8

=> v = 48 mph

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Re: Speed of bus [#permalink] New post   26 Mar 2013, 22:35
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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.
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   31 Dec 2013, 09:56
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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

Answer is C

Gimme some Kudos will ya?

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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   30 Sep 2015, 15:19
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Why is the bus only doing 18 mph? Is it some kind of special GMAT bus?
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A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   01 Oct 2015, 04:29
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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
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   02 Oct 2015, 11:53
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
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   18 Nov 2016, 09:49
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
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   20 Jun 2020, 01:49
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


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
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   10 Jan 2021, 22:42
(5+3)(x-30)= 3x
8(x-30)= 3x
8x-240=3x
8x-240-3x=0
5x-240=0
x=240/5
x= 48

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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink] New post   23 Aug 2022, 23:20
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]
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