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M18-02

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Bunuel
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M18-02 [#permalink] New post   16 Sep 2014, 01:02
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77% (02:51) correct 23% (03:03) wrong based on 196 sessions
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A 400-meter runner took 4 seconds longer to cover the first half of the distance than he did for the second half. If he completed the 400-meter race in 50 seconds, what was his average (arithmetic mean) speed for the first 200 meters?

A. \(24 \frac{1}{3} \text{ kmh}\)
B. \(25 \frac{1}{3} \text{ kmh}\)
C. \(26 \frac{2}{3} \text{ kmh}\)
D. \(27 \frac{2}{3} \text{ kmh}\)
E. \(29 \frac{1}{2} \text{ kmh}\)
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Bunuel
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Re M18-02 [#permalink] New post   16 Sep 2014, 01:02
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Official Solution:

A 400-meter runner took 4 seconds longer to cover the first half of the distance than he did for the second half. If he completed the 400-meter race in 50 seconds, what was his average (arithmetic mean) speed for the first 200 meters?

A. \(24 \frac{1}{3} \text{ kmh}\)
B. \(25 \frac{1}{3} \text{ kmh}\)
C. \(26 \frac{2}{3} \text{ kmh}\)
D. \(27 \frac{2}{3} \text{ kmh}\)
E. \(29 \frac{1}{2} \text{ kmh}\)


Let's denote \(x\) as the time the runner spent on the first 200 meters. Then, we have the equation \(x + (x - 4) = 50\), from which we find \(x = 27\) seconds. The athlete covered the first 200 meters in 27 seconds, yielding an average speed of \(\frac{200}{27}\text{ ms}\) or \(\frac{200}{27} * \frac{3600}{1000} = 26 \frac{2}{3} \text{ kmh}\).


Answer: C
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Re: M18-02 [#permalink] New post   24 Jun 2015, 08:52
Hi Bunel,

can i ask you a quick way of making the last calculation: (200/27∗3600/1000)=26 2/3 kmh?

i got stuck at this point :(
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Re: M18-02 [#permalink] New post   24 Jun 2015, 10:37
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alefal wrote:
Hi Bunel,

can i ask you a quick way of making the last calculation: (200/27∗3600/1000)=26 2/3 kmh?

i got stuck at this point :(


\(\frac{200}{27} * \frac{3600}{1000} =\)

\(\frac{200*3600}{27*1000} =\)

Reduce by 1000: \(\frac{2*360}{27} =\)

Reduce by 9: \(\frac{2*40}{3} =\)

\(=\frac{80}{3}=26 \frac{2}{3} \text{ kmh}\)
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Re: M18-02 [#permalink] New post   24 Jun 2015, 10:48
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Re: M18-02 [#permalink] New post   24 Jun 2015, 10:52
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alefal wrote:
Danke


Gern geschehen! :-D
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Re: M18-02 [#permalink] New post   12 Feb 2017, 13:25
Can you pls explain how did you get 3600/1000?
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Re: M18-02 [#permalink] New post   13 Feb 2017, 02:16
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GangaAnupam wrote:
Can you pls explain how did you get 3600/1000?


This is to transform meter per second to kilometre per hour.

200 meters = 200/1000 kilometres and 27 seconds = 27/3600 hours.


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Re: M18-02 [#permalink] New post   02 Jun 2017, 07:49
Good question, lots of areas to make mistakes. I skimmed too fast and did the calculation for the second part.

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Re: M18-02 [#permalink] New post   05 Jun 2017, 16:21
wow...the math is easy in this question, but i couldn't do it because i didn't know the meter conversion formula. i am in the US and this is not a common unit of measurement.

would a US-based GMAT test us on meters? or, what is more common, miles?
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Re: M18-02 [#permalink] New post   06 Jun 2017, 09:36
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gatorwageralpha wrote:
wow...the math is easy in this question, but i couldn't do it because i didn't know the meter conversion formula. i am in the US and this is not a common unit of measurement.

would a US-based GMAT test us on meters? or, what is more common, miles?


The question itself will supply the relative conversions. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ... If kilometre/meter conversion is not a common knowledge in US, this too will be provided.

Check other Conversion problems to practice in Special Questions Directory.
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Re: M18-02 [#permalink] New post   27 Sep 2023, 11:04
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M18-02 [#permalink]
27 Sep 2023, 11:04
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