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M09-09

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The train consists of 6 carriages, 20 meters long each. The gap between the carriages is 1 meter. If the train is moving at a constant speed of 60 km/h, how much time will it take the train to run through a 1 kilometer tunnel?

A. \(1\frac{1}{8}\) minutes
B. \(1\frac{1}{2}\) minutes
C. \(1\frac{3}{4}\) minutes
D. 2 minutes
E. \(2\frac{1}{4}\) minutes
[Reveal] Spoiler: OA

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Official Solution:

The train consists of 6 carriages, 20 meters long each. The gap between the carriages is 1 meter. If the train is moving at a constant speed of 60 km/h, how much time will it take the train to run through a 1 kilometer tunnel?

A. \(1\frac{1}{8}\) minutes
B. \(1\frac{1}{2}\) minutes
C. \(1\frac{3}{4}\) minutes
D. 2 minutes
E. \(2\frac{1}{4}\) minutes


The length of the train is \(6*20\) plus five 1 meter gaps, so it's \(6*20+5=125\) meters;

The length that should be traveled by train is \(1+0.125=1.125\) kilometers;

\(\text{Time}=\frac{\text{Distance}}{\text{Rate}}=\frac{1.125}{60}\) hours or \(\frac{1.125}{60}*60=1.125=1\frac{1}{8}\) minutes.


Answer: A
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Re: M09-09 [#permalink]

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New post 14 Mar 2015, 04:56
Bunuel wrote:
Official Solution:

The train consists of 6 carriages, 20 meters long each. The gap between the carriages is 1 meter. If the train is moving at a constant speed of 60 km/h, how much time will it take the train to run through a 1 kilometer tunnel?

A. \(1\frac{1}{8}\) minutes
B. \(1\frac{1}{2}\) minutes
C. \(1\frac{3}{4}\) minutes
D. 2 minutes
E. \(2\frac{1}{4}\) minutes


The length of the train is \(6*20\) plus five 1 meter gaps, so it's \(6*20+5=125\) meters;

The length that should be traveled by train is \(1+0.125=1.125\) kilometers;

\(\text{Time}=\frac{\text{Distance}}{\text{Rate}}=\frac{1.125}{60}\) hours or \(\frac{1.125}{60}*60=1.125=1\frac{1}{8}\) minutes.


Answer: A


Hi Bunuel,

Your question is a little bit ambiguous.
When one say that the train is entering into tunnel, the total time train was inside the tunnel is the time taken by the train when 1st coach enters the tunnel till the last coach exits the tunnel.

That makes 1 km + 125 + 125.

I don't know why did you pick 1 km + 125 m ?

Can you please clarify?

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How do you arrive at this step:

"The length that should be traveled by train is 1+0.125=1.125 kilometers;"

I understand the steps before and after that, just not this part - thanks!

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New post 22 Nov 2015, 04:21
LostinNY wrote:
How do you arrive at this step:

"The length that should be traveled by train is 1+0.125=1.125 kilometers;"

I understand the steps before and after that, just not this part - thanks!


0.125km ---------------------------------------------- 1km
------|------------------------------------------------|

In red is a train and in blue a tunnel. The whole train to run through the tunnel, it should travel the length of a train plus the length of the tunnel.
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Re: M09-09 [#permalink]

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New post 18 Feb 2016, 07:28
Hi Bunuel,

I'm struggling to understand why/how you're multiplying by 60 to cancel out the rate.

Can you please explain?

Thanks in advance.

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New post 09 Mar 2016, 00:11
Hi Bunnel,

Can you illustrate it more please ?

Thanks
Eman

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New post 14 Jul 2017, 06:28
I think this is a high-quality question and I don't agree with the explanation. the answer is incorrect. total distance traveled by train to cross the tunnel will be 1.25 KM not 1.125. we cannot chopp of the crarriages length at exit of the tunnel

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New post 14 Jul 2017, 06:39
Sushilait84 wrote:
I think this is a high-quality question and I don't agree with the explanation. the answer is incorrect. total distance traveled by train to cross the tunnel will be 1.25 KM not 1.125. we cannot chopp of the crarriages length at exit of the tunnel


How did you get 1.25 km? We ARE counting the length of the tunnel + the length of the train.

The length of the train is \(6*20\) plus five 1 meter gaps, so it's \(6*20+5=125\) meters;

The length that should be traveled by train is \(1+0.125=1.125\) kilometers (1 kilometer and 125 meters);
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Collection of Questions:
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New post 09 Oct 2017, 05:44
This is a poor quality question. The total length travelled should be 1000+125+125

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New post 08 Nov 2017, 11:20
That is from when the front enters the tunnel to when the front exits the tunnel. But the body of the train is still 125meters inside the tunnel.

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Re: M09-09   [#permalink] 08 Nov 2017, 11:20
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