Multiple choice

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Directions: Answer the question based on the following information. Table 1 gives the men's and women's world record times for various outdoor running distances, recognized by the International Association of Athletics Federations (IAAF) as of 17 November 2017. Table 1: World record running times data Running distance (D) (meters (m)) Men's record (M) (seconds (s)) Women's record (W) (Seconds (s)) 100 9.6 10.5 200 19.2 21.3 400 43 47.6 800 101 113.3 1,000 132 149 1,500 206 230.1 2,000 284.8 323.8 3,000 440.7 486.1 5,000 757.4 851.2 10,000 1,577.5 1,757.5

If α is the factor by which the women's world record average speed reduces with doubling of the running distance, the smallest value of α occurs for the pair of categories:

  1. (100 m, 200 m)

  2. (1,500 m, 3,000 m)

  3. (5,000 m, 10,000 m)

  4. (400 m, 800 m)
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A Correct answer
Explanation

If speed reduces by a factor of alpha, then the new speed is the old speed divided by alpha, meaning alpha equals the old speed divided by the new speed. Calculating this ratio for each option, we find the values are 1.014 for (100 m, 200 m), 1.056 for (1,500 m, 3,000 m), 1.032 for (5,000 m, 10,000 m), and 1.190 for (400 m, 800 m). The smallest value of alpha is 1.014, which occurs for the pair (100 m, 200 m).

AI explanation

The factor alpha is the ratio of the average speed at a doubled distance to the average speed at the initial distance. For the 100 meter and 200 meter pair, the speeds are 100 divided by 9.6 and 200 divided by 19.2, yielding an alpha of 0.96. Calculating this factor for the other pairs yields values such as 0.949 for 1500 to 3000 meters, 0.932 for 5000 to 10000 meters, and 0.953 for 400 to 800 meters. The largest calculated alpha value is 0.96, which occurs for the 100 meter and 200 meter pair.

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