Multiple choice

Baron drove from his house to his cousin's house and then drove back from there to his house. He took two different routes, one for going and one for coming. While driving from his house to his cousin's house, he drove at a speed of 36 mph, and while returning from his cousin's house to his house, his speed was 48 mph. What was his average speed for the total distance? (1) The distance of the first route was 24% of the entire distance he travelled. (2) The distance of the second route was 100 miles.

  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 statement 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. Let d1 and d2 be distances. Total time = d1/36 + d2/48. Statement 1 gives d1 = 0.24 * (d1+d2), which allows expressing d1 in terms of d2. This is sufficient to calculate the average speed.

AI explanation

The average speed formula for a journey with different distances is total distance divided by the sum of (individual distances divided by their respective speeds). Statement 1 provides the ratio of the two route distances as 24 percent to 76 percent, simplifying to a ratio of 6 to 19, which allows you to set the distances as 6x and 19x and calculate the average speed independently of x, yielding a single numerical value. Statement 2 only gives the length of the second route without providing the length of the first route, making it impossible to calculate the total travel time or the average speed. Therefore, statement 1 alone is sufficient, while statement 2 alone is not.

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