A taxi leaves Point A 5 hours after a bus left the same spot : GMAT Problem Solving (PS)
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# A taxi leaves Point A 5 hours after a bus left the same spot

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

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18 Apr 2011, 04:45
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Difficulty:

35% (medium)

Question Stats:

75% (02:41) correct 25% (02:24) wrong based on 420 sessions

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Mar 2013, 04:38, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]

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31 Dec 2013, 08:56
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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

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

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01 Oct 2015, 03:29
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Expert's post
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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18 Apr 2011, 06:03
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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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18 Apr 2011, 06:31
1
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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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18 Apr 2011, 06:17
Thanks! even i got 48 as the answer
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18 Apr 2011, 06:39
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lets start again

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18 Apr 2011, 07:16
Let v be the speed of the taxi

3v = (v-30)8

=> v = 48 mph

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26 Mar 2013, 21:35
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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]

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30 Sep 2015, 00:04
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]

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30 Sep 2015, 14:19
Why is the bus only doing 18 mph? Is it some kind of special GMAT bus?
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]

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02 Oct 2015, 10:53
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
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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]

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06 Oct 2016, 20:12
Hello from the GMAT Club BumpBot!

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Re: A taxi leaves Point A 5 hours after a bus left the same spot [#permalink]

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18 Nov 2016, 08:49
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

Re: A taxi leaves Point A 5 hours after a bus left the same spot   [#permalink] 18 Nov 2016, 08:49
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