How much faster does ²³⁵UF₆effuse than ²³⁸UF₆? A) 1.006 times as fast B) 1.004 times as fast C) 1.013 times as fast D) 1.009 times as fast E) 1.018 times as fast

Question

Quizplus · Accepted Answer

To compare the speed, we need to count the number of each letter in both codes. S1U1P1235S1S1P0UFS1U1B16 has 9 S's, 4 U's, 4 1's, 2 2's, 2 3's, 1 5, 1 P, 1 F, and 1 B. S1U1P1238S1S1P0UFS1U1B16S1U1B0 has 11 S's, 4 U's, 4 1's, 2 2's, 1 3, 1 5, 1 P, 1 F, and 2 B's. We can see that the first code has a "5" instead of a "0" and the second code has an extra "B" at the end. As neither of those affect the speed, we can ignore them. The only difference between the two codes is that the first code has 9 S's and the second code has 11 S's. Therefore, the second code is 11/9 = 1.222... times as fast as the first code. However, we need to subtract 1 from this calculation because the question asks how much faster the second code is compared to the first code (not how much faster the second code is relative to the first code). So the answer is 1.222... - 1 = 0.222..., which rounded to three decimal places is 0.223. Finally, we add 1 to this answer because the question asks for "times as fast." So the final answer is 1.223 times as fast, which rounded to three decimal places is 1.004. Therefore, the best choice is B.

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How Much Faster Does ²³⁵UF₆effuse Than ²³⁸UF₆