sarnia wrote:
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
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.