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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, 05:45

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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.

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.

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.

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

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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.

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

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30 Sep 2015, 01:04

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).

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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]

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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
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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, 21:12

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).

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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, 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