Multiple choice

On a certain delivery route, Rafael biked at m miles per hour for 1.5 hours and then at n miles per hour for the next 2.5 hours. What was his average speed, in miles per hour, for the entire trip? (1) 1.5m + 2.5n = 160 (2) n = m + 20

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER alone is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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A Correct answer
Explanation

Average speed = Total Distance / Total Time. Total Distance = 1.5m + 2.5n. Total Time = 1.5 + 2.5 = 4 hours. Average speed = (1.5m + 2.5n) / 4. Statement (1) gives 1.5m + 2.5n = 160, so average speed = 160 / 4 = 40. Statement (2) relates n and m but does not provide the total distance.

AI explanation

The average speed formula is total distance divided by total time, so here it is (1.5m + 2.5n) / (1.5 + 2.5) = (1.5m + 2.5n) / 4. Statement (1) gives the exact value of the numerator as 160, allowing you to calculate the average speed as 160 / 4 = 40 miles per hour. Statement (2) only relates m and n without giving the total distance, so it is insufficient. Statement (1) alone is sufficient.

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