M18-02

Question

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} 	ext{ kmh}  
B.  25 \frac{1}{3} 	ext{ kmh}  
C.  26 \frac{2}{3} 	ext{ kmh}  
D.  27 \frac{2}{3} 	ext{ kmh}  
E.  29 \frac{1}{2} 	ext{ kmh}

Bunuel · Answer

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} 	ext{ kmh}  
B.  25 \frac{1}{3} 	ext{ kmh}  
C.  26 \frac{2}{3} 	ext{ kmh}  
D.  27 \frac{2}{3} 	ext{ kmh}  
E.  29 \frac{1}{2} 	ext{ 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}	ext{ ms}  or  \frac{200}{27} * \frac{3600}{1000} = 26 \frac{2}{3} 	ext{ kmh} .

Answer: C

alefal · Answer

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

Bunuel · Answer

\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} 	ext{ kmh}

alefal · Answer

Danke

Bunuel · Answer

Gern geschehen! :-D

GangaAnupam · Answer

Can you pls explain how did you get 3600/1000?

Bunuel · Answer

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

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

Check other  Conversion problems  to practice from our  Special Questions Directory .

gmathopeful19 · Answer

Good question, lots of areas to make mistakes. I skimmed too fast and did the calculation for the second part.

Posted from my mobile device

gatorwageralpha · Answer

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?

Bunuel · Answer

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 .

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

maddscientistt · Answer

Hi  Bunuel ,

I understood the given straight forward solution,

But solving this using naive method I'm getting struck at one point, can you please help me here,

firstly,

Total Average =  \frac{Total Distance}{Total Time} 
Total Average = 400/50 = 8

Now,

let t = time taken during the second half 
t+4 becomes the time taken during the first half

Finally to be found is  \frac{200}{(t+4)}  i.e, average speed for the first half

using the above same formula,

Total Average = 8 =  \frac{400}{200/(t+4) * 200/t}

8 =     *   ]

3 =  \frac{t(t+4)}{2t+4}

3 * (2t + 4) = t^2 + 4t 
 t^2 - 2t - 12 = 0

Now I'm struck, how to proceed further ..

I know, I should be making use of all data given in stem but when forgot to get the time using (t + 4) + t = 50 to get t

Bunuel · Answer

Sorry, but I don't understand what you're trying to do there. I also don't see why anyone would solve for t that way when you can easily find it using (t + 4) + t = 50.

bibhuti750 · Answer

I like the solution - it’s helpful.

NemXsammy · Answer

I like the solution - it’s helpful.

NemXsammy · Answer

I like the solution - it’s helpful.

M18-02

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