Two Runners

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If Runner A followed Runner B down a portion of track that is mile long, how many seconds did it take Runner A to run the track?

(1) Runner A ran onto the track 10 seconds after Runner B ran onto the track and ran off the track 8 seconds after Runner B ran off the track.

(2) Runner B ran the track at a constant speed of 9 miles per hour.

Review: Two Runners




Explanation

We have a speed problem here, so we may be working with the equation, But we also have a comparison. So, on one hand, we might be able to answer this information by getting complete information; on the other, we might be able to answer it with information that isn't complete, but which has the right comparative information. On to the data statements, which we first look at separately. Statement (1) defines the time Runner A took to run the track in terms of the time it took Runner B. But we don't know that latter quantity, so Statement (1) is insufficient. Next we look at Statement (2) alone. It gives us Runner B's speed, which allows us to calculate Runner B's time based on the length of the track. But when we look at Statement (2) alone, we have no information about how to relate this knowledge about Runner B to Runner A. So Statement (2) is insufficient. Combining the statements, we have what we need: Runner A's time in terms of Runner B's time, and Runner B's time. So the statements are sufficient together.

The correct answer is (C).


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