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Alek went for a walk. D(t) models the distance Alek walked (in kilometers) after t hours. What does the statement D(0.5) < D(1)-D(0.5) mean? Choose 1 answer: (A) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer. (B) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour. (C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.

Alek went for a walk.\newlineD(t)D(t) models the distance Alek walked (in kilometers) after tt hours.\newlineWhat does the statement D(0.5) < D(1)-D(0.5) mean?\newlineChoose 11 answer:\newline(A) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.\newline(B) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.\newline(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.

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Full solution

Q. Alek went for a walk.\newlineD(t)D(t) models the distance Alek walked (in kilometers) after tt hours.\newlineWhat does the statement D(0.5)<D(1)−D(0.5)D(0.5) < D(1)-D(0.5) mean?\newlineChoose 11 answer:\newline(A) The time it took Alek to walk the first half kilometer is shorter than the time it took him to walk the following half kilometer.\newline(B) The distance Alek has walked after walking for an hour is greater than the distance he has walked after half an hour.\newline(C) The distance Alek walked during the first half hour is shorter than the distance he walked during the following half hour.
  1. Analyze the statement: Let's analyze the statement D(0.5) < D(1) - D(0.5).\newlineD(t)D(t) is the distance Alek walked after tt hours.\newlineD(0.5)D(0.5) is the distance Alek walked after half an hour.\newlineD(1)D(1) is the distance Alek walked after one hour.\newlineThe statement is comparing the distance walked in the first half hour to the distance walked in the second half hour.
  2. Interpret D(1)−D(0.5)D(1) - D(0.5): To understand the comparison, we need to interpret D(1)−D(0.5)D(1) - D(0.5).D(1)−D(0.5)D(1) - D(0.5) represents the distance walked from the half-hour mark to the one-hour mark. If D(0.5) < D(1) - D(0.5), it means that the distance Alek walked in the second half hour is greater than the distance he walked in the first half hour.
  3. Match interpretation with choices: Now, let's match this interpretation with the given choices.\newline(A) This choice talks about time, not distance, so it is not relevant to our comparison.\newline(B) This choice is incorrect because it compares the total distance after one hour to the distance after half an hour, not the distances walked in each half-hour segment.\newline(C) This choice correctly states that the distance walked during the first half hour is shorter than the distance walked during the following half hour, which matches our interpretation of the statement.

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