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# Two guns were fired from the same place at an interval of 10

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Manager
Joined: 17 Mar 2010
Posts: 183
Two guns were fired from the same place at an interval of 10 [#permalink]

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06 May 2010, 05:34
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Difficulty:

95% (hard)

Question Stats:

47% (03:15) correct 53% (03:27) wrong based on 206 sessions

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Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

A. 19.8
B. 58.6
C. 59.4
D. 111.8

Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Do let me know how log does it take for you and also if this is worth getting in GMAT.
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 39662
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 06:54
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amitjash wrote:
Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

a) 19.8
b) 58.6
c) 59.4
d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

In 30 sec sound covers the same distance as train in 10 min.

In 30 seconds sound covers 330*30=9900m=9.9 km, --> hence in 10 minutes train covers 9.9 km --> in 1 hr train covers 9.9*6 km= 59.4 km.

I guess for GMAT it's 700+ question.

Similar questions to practice:
each-day-a-man-meets-his-wife-at-the-train-station-after-93545.html
a-man-arrives-at-a-railway-station-90mins-before-the-time-at-100073.html
ray-who-lives-in-the-countryside-caught-a-train-for-home-ea-84295.html
mrs-robbins-started-half-an-hour-later-than-usual-for-market-104482.htmL

Hope it helps.
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Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 07:34
Wow! this on GMAT will be like writing a Physics exam......

typical Doppler effect question
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Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 09:36
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Bunuel wrote:
amitjash wrote:
Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

a) 19.8
b) 58.6
c) 59.4
d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

In 30 sec sound covers the same distance as train in 10 min.

In 30 seconds sound covers 330*30=9900m=9.9 km, --> hence in 10 minutes train covers 9.9 km --> in 1 hr train covers 9.9*6 km= 59.4 km.

I guess for GMAT it's 700+ question.

Hi Bunuel, could you please explain more about the way you think this problem.
Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 10:00
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netrix wrote:
Bunuel wrote:
amitjash wrote:
Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

a) 19.8
b) 58.6
c) 59.4
d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

In 30 sec sound covers the same distance as train in 10 min.

In 30 seconds sound covers 330*30=9900m=9.9 km, --> hence in 10 minutes train covers 9.9 km --> in 1 hr train covers 9.9*6 km= 59.4 km.

I guess for GMAT it's 700+ question.

Hi Bunuel, could you please explain more about the way you think this problem.
Thanks!

If the person were static he would hear ("meet") the sound in 10.5 minutes, but he heard ("met") the sound in 10 minutes, and that's because during these 10 minutes the person was moving towards the sound. Thus these 10 minutes of person moving "saved" the sound its 0.5 minutes of moving.

OR: let's say (imagine) the distance between the shooting point and person when the second shot was made was $$d$$. We are told that this distance would be covered in 10.5 minutes if person were static: $$d=10.5s$$ ($$s$$ speed of sound).

But because person was was moving towards the sound they "met" in 10 minutes, which means that the distance $$d$$ was covered in 10 minutes at their combined speed. Their combined speed was $$s+t$$ ($$t$$ the speed of person/train): $$d=10(s+t)$$.

$$d=10.5s=10(s+t)$$ --> $$0.5s=10t$$.

Hope it helps.
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Joined: 26 Feb 2010
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Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 10:08
Excellent explanation!!
Much more clear now.
Thanks!
+1 Kudo for you.
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Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 13:22
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I assumed speed of sound as 300 as given and was not getting correct answer.Pls correct it as 330

Another easy way.

Suppose train is still, then the person will hear the sound in 10min 30 secs = 630s

i.e. if relative speed is 330 then time = 630
if relative speed is 330+x then time = 600 as both the moving opp to each other.

=>
630*330 = 600(330+x) I have actually equated the relative distances in the two cases.

this gives x as 33/2 m/s or 59.4 km/hr

Edit: Typo mistake 330*

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Last edited by gurpreetsingh on 06 May 2010, 14:17, edited 1 time in total.
Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 14:10
gurpreetsingh wrote:
I assumed speed of sound as 300 as given and was not getting correct answer.Pls correct it as 330

Another easy way.

Suppose train is still, then the person will hear the sound in 10min 30 secs = 630s

i.e. if relative speed is 330 then time = 630
if relative speed is 330+x then time = 600 as both the moving opp to each other.

=>
630*330 = 600(300+x) I have actually equated the relative distances in the two cases.

this gives x as 33/2 m/s or 59.4 km/hr

Excellent way too gurpreesingh! Very clear

Can be a typo in your formula? it says
630*330 = 600(300+x)
should be
630*330 = 600(330+x)
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Concentration: Technology, Entrepreneurship
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GMAT 2: 710 Q50 V35
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 14:19
Thanks for pointing it out; I have modified the post.
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Manager
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Posts: 79
Location: Argentina
Re: Is this question too tough for GMAT level? [#permalink]

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06 May 2010, 14:31
thank to you for the explanation!
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Joined: 29 Aug 2011
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Re: Is this question too tough for GMAT level? [#permalink]

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11 Mar 2012, 06:20
amitjash wrote:
Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

a) 19.8
b) 58.6
c) 59.4
d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

Let the time when first bullet was heard by the person be t0 = 0 mins
Now train moves with a certain speed x m/s.
Another shot was fired after 10m 30s, since the train was already moving in towards the place where shots were fired, it could here it little earler i.e., 10 mins. In 10 mins the train travelled certain distance too. Also, had the train been stationary, it would have heard the sound of the shot after 10mins 30 seconds only.

It thus implies that distance travelled by train in 10 mins is equal to distance travelled by bullet in 30s. Hence the equation

330 m/s * 30s = 600s * x m/s
x = 33/2 m/s => 59.4 kmph
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Re: Two guns were fired from the same place at an interval of 10 [#permalink]

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04 Aug 2013, 13:05
Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

I'm not entirely sure I understand the wording. Are they trying to say that gun 1 was fired at T=0 then gun 2 fired at T=10:30?

If that's the case, the person in the approaching train moved towards the two guns enough so that instead of the sound taking 10 minutes & 30 seconds to reach him, it took just 10 minutes. In other words, he moved towards the guns enough so it takes 30 seconds less for the sound to travel to him.

Time it takes the sound to reach him originally: 10:30 = 630 seconds * 330 m/seconds = 207,900 meters
Time it takes the sound to reach him after he has moved towards the guns: 10:00 = 600 seconds * 330 m/seconds = 198,000

Difference = 9900m.

So the train moved 9900m closer to the guns in 10 minutes time. Therefore at a constant rate he would have moved 9900*10/1*6/1hour = 9900*60 = 59400m/hour = 59.4 km/h

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Re: Two guns were fired from the same place at an interval of 10 [#permalink]

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21 Aug 2014, 06:44
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Re: Two guns were fired from the same place at an interval of 10 [#permalink]

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02 Sep 2015, 01:32
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Re: Two guns were fired from the same place at an interval of 10 [#permalink]

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09 Jul 2016, 04:52
I was just going through the explanations, but what I dont understand is that if the shot was fired 10.5 mins after the first one, how can the man hear the second shot even before it was shot!

Bunuel wrote:
Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330m/s is:

a) 19.8
b) 58.6
c) 59.4
d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

In 30 sec sound covers the same distance as train in 10 min.

In 30 seconds sound covers 330*30=9900m=9.9 km, --> hence in 10 minutes train covers 9.9 km --> in 1 hr train covers 9.9*6 km= 59.4 km.

I guess for GMAT it's 700+ question.[/quote]
Hi Bunuel, could you please explain more about the way you think this problem.
Thanks![/quote]

If the person were static he would hear ("meet") the sound in 10.5 minutes, but he heard ("met") the sound in 10 minutes, and that's because during these 10 minutes the person was moving towards the sound. Thus these 10 minutes of person moving "saved" the sound its 0.5 minutes of moving.

OR: let's say (imagine) the distance between the shooting point and person when the second shot was made was $$d$$. We are told that this distance would be covered in 10.5 minutes if person were static: $$d=10.5s$$ ($$s$$ speed of sound).

But because person was was moving towards the sound they "met" in 10 minutes, which means that the distance $$d$$ was covered in 10 minutes at their combined speed. Their combined speed was $$s+t$$ ($$t$$ the speed of person/train): $$d=10(s+t)$$.

$$d=10.5s=10(s+t)$$ --> $$0.5s=10t$$.

Hope it helps.[/quote]
Re: Two guns were fired from the same place at an interval of 10   [#permalink] 09 Jul 2016, 04:52
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