90% of a Trip

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During a particular trip, how much time had elapsed once 90% of the total distance of the trip had been traveled?

(1) The total distance of the trip was 40 miles and the total time elapsed was exactly 4 hours.

(2) The average speed of the trip was exactly 10 miles per hour.

Review: 90% of a Trip




Explanation

Reading the question, we can observe that, if we are traveling at a constant speed on this trip, then it will have taken 90% of the time of the trip to travel 90% of the distance. That might be what the data statements will go for. However, we are not specifically told yet that we have traveled at a constant speed, and that may be significant. On to the data statements, separately first.

Statement (1) plays into our expectations: it allows us to infer the time of the trip, but we don't know whether the speed was constant. We might have been in standstill traffic for 90% and cruised for the last 10%, or it could have been a constant speed. Those two cases yield different answers, so we don't have sufficient information to answer the question definitively. Statement (1) is insufficient.

Statement (2) gives us the trip's average speed, which is a ratio of total distance to total time. The fact that it's "exactly" 10 miles per hour doesn't change the fact that it's an average speed that we are talking about, not a constant speed. The case of standstill traffic followed by a rocket blast is still a possibility. Therefore, Statement (2) is insufficient.

Combining statements doesn't allow us to know whether or not the speed was constant. It might have been constant, and it might not have been, so we have insufficient information to answer the question definitively.

The correct answer is (E).


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