In a 200-meter race, the winner crossed the finish line 2.5

Question

Hi,
In a 200-meter race, the winner crossed the finish line 2.5 seconds ahead of the second-place runner. How far back was the second-place runner when the winner crossed the finish line?
1.The winnerтАЩs time was 22.5 seconds
2.The second-place runner ran 8 meters per second until the winner crossed the line
My answer : C, The official answer :D
Am I wrong :help2

Am I wrong :help2

wonder_gmat · Answer

I vote for  D .

(1) Since we know the timing of the winner we can find that of the second place winner. And thus, the distance between them at any given time.
(2) We're given the speed of the runner so we can find the distance at any given time.

dj · Answer

from 1st we'll know:
distance winner travelled in 2.5 secs = (200/22.5)*2.5
thus, (original distance - D in 2.5 sec) gives you the penultimate's position. A suffice.

from 2nd:
time for which next to the winner ran = 200/8=25 sec
thus, winner traveled 25-2.5 = 22.5 sec. This is same as A.

Both are sufficient. Hence D.

sarnia · Answer

Got it. Thanks :-D

AkamaiBrah · Answer

I don't agree with the official answer. This is only true if both runners ran AT A CONSTANT SPEED throughout. This is not necessarily true, nor is it a reasonable assumption. During a sprint race, race, both racers slow down almost immediate. In a longer race, there is considerable manuvering. 

1) Here is an extreme situation. Suppose the winner ran a "normal" race and finished in 22.5 seconds. The second place guy ran just a smidgen slower so at the time of the winner crossing, the 2nd guy was only a foot (or inch or centimeter) back. However, just then he seizes up, then 2.5 seconds to recover and cross. Hence, just because the difference in times are 2.5 seconds, unless we know the average speed of the second guy over those 2.5 seconds, we cannot determine how far back he was at the time. Therefore, 1) IS NOT SUFFICIENT

2) The second guy runs a constant 8 meter per second at the time the winner finishes. Since we do not know how much time the winner takes, we cannot determine how far away from the finish line is in in order. Nor do we know how fast or slow he runs once the winner crosses the finish line -- we only know that he makes up that distance in 2.5 seconds. Hence, there is no way to know how far back the 2nd guy is when the first guy finishes. 

Both: We know the first guy finished in 22.5 seconds by (1). Since by (2), the second guy ran at a constant speed of 8 m/s for that time, we know that at the time of the winner crossing, the 2nd guy is at the 22.5 x 8 = 170m mark. Hence, assuming that runner 2 is actually running in the direction of the track (ha ha) both statements are needed and  IMO, Sarnia is correct and the answer is C.

maverick_ucdc · Answer

The official answer is correct.

If we have to agree with ur explainations then the answer should be E rather than C, if u r going to consider every instance, then even all the 2 statements are not sufficient. So the equation here should not be:
Distance = Speed* Time
But
Distance = Speed*time + .5 (acceleration) * time^2

And throughout the problem, the term acceleration is not defined neither is the time that is required to accelerate.




Look at the following problem:
An automobileтАЩs gasoline mileage varies, depending on the speed of the automobile, between 18.0 and 22.4 miles per gallon, inclusive. What is the maximum distance, in miles, that the automobile could be driven on 15 gallons of gasoline?

Then we could assume that the car would travel some distance due to the momentum of the car even after the gas tank is dry based on its final speed, friction of the road & the slope of the road will be the only resistence .

AkamaiBrah · Answer

2.The second-place runner ran 8 meters per second until the winner crossed the line 

This can be reasonably interpreted to mean either the runner ran at a constant 8 m/s over a period T or an average 8 m/s over a period T. Either way, he will travel the same distance over time T or exactly 8 * T meters. Let's assume the second interpretation, which is looser than the first. Even if he stops, starts again, etc. IF HE AVERAGES 8 m/s over T then he will must travel exactly 8*T at time T by simple definition of average rate. 

1. this tells exactly when time T is. Now we know how far the second runner ran = 8 * T = 170. Since we know that the track in 200 meter long, at this instant, the runner is 30 meters back as the first runner is at the finish line. That is the answer to the question. 

YOu are correct that we don't know any thing about acceleration. This is why neither statement is sufficient alone. However, in order to calculate an average rate, we do need to know something about the state of being at a particular "checkpoint" in time. Given an averave rate over time T, we ONLY know distances at time T. This is our "checkpoint" Since the time frame of the question is exactly at time T (the instant the runner crosses the finish line) the information given in the two statements together is sufficient and I maintain that the answer is C.

maverick_ucdc · Answer

Well we disagree again, but anyway I will not say that u r wrong - logically I will accept ur explaination because practically u r closer to real world situation.

BUT in regard to this problem, its a very simple problem and we are tryingn to over analyze it.

Try it like this.

2 guys ran for 200m, 1 was faster other was not. 1 finished in x sec and 2 finsihed in y secs.

Now try filling in the x and y - its becomes simple problem for the sake of GMAT

Cheers

AkamaiBrah · Answer

I am not overanalyzing the problem. Just trying to point out how to recognize  what information is needed   in order to  answer the question  given (exactly the point of DS questions). 

Method in nutshell: We want to know Dist of racer 2 at time T so we can subtract this from 200 to get the answer. Dist = Average rate * T. Hence we need both T and averate of racer 2 to get answer.

1) gives us T
2) gives us ave rate of racer 2
Answer is C. 

Note: Since we know nothing about racer2's speed (absolute or average) after time T, the fact that he finishes 2.5 seconds later is completely useless and should be ignored (we don't even care if he finishes or not). Hence your "the answer is simply x-y" is wrong if x and y refer to finish times repectively

The "official" answer of D is only correct, as I stated before, if one makes unjustified assumptions about the speed of the racers -- i.e, that racer 2 runs at a constant speed throughout. ONe of the big things that DS questions tests for is the making of unwarranted assumptions, of which this would clearly be one. 

P.S. I don't consider published answers with no attribution or explantions on Korean or Chinese web sites "official." Should you?

gmatblast · Answer

I do not think AkmaiBrah has overanalyzed the problem. I guess that is the only and correct way to analyze this problme. All that is required to solve this problem is just a clear understanding of the concept of average speed. I again agree with AkmaiBrah that the answer is C.

wonder_gmat · Answer

I have my velocity and distance formula(s) still in-line and honestly answer D came to my mind. Not sure if this problems needs the kind of deep analysis or ripping to pieces like this. But hey the floor is open for discussion so hava-ball...
:pilot

AkamaiBrah · Answer

You can use formula to get distance if you know BOTH time and rate. However, you do NOT know the rate of racer 2  once racer 1 crosses the finish line.  Hence, you cannot calculate position of racer 2 going backward from finish line to current position, only forward from starting line up to current position.

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In a 200-meter race, the winner crossed the finish line 2.5

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