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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

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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, 04:29

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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 _________________

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

Expert's 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 _________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford +1 Kudos if you find this post helpful

gmatclubot

Re: A taxi leaves Point A 5 hours after a bus left the same spot
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02 Oct 2015, 11:53

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