Alice leaves the Malefeco Corporation building and travels due east fo

ScottTargetTestPrep I understand all of your explanations in your comments. Can you please help break down calculations for this problem?

Suppose Alice’s speed is 2v and Joseph’s speed is v.

In total, Alice runs due east for 20 + 10 = 30 minutes and due south for 30 minutes. Alice’s distance to Malefeco is given by the length of hypotenuse in an equilateral right triangle where the legs have length 30*2v = 60v; therefore, Alice’s distance to Malefeco, in terms of v, is (60√2)v.

Joseph runs due North for 40 minutes and due West for 30 minutes. Joseph’s distance to Malefeco is given by the length of hypotenuse in a 3-4-5 right triangle where the legs have length 30v and 40v; therefore Joseph’s distance to Malefeco, in terms of v, is 50v.

The ratio of Alice’s distance to Joseph’s distance is (60√2)v / 50v = 6√2 / 5. Approximating √2 as 1.4, we see that the ratio is (6*1.4)/5 = 8.4/5 = 1.68. Thus, Alice’s distance must be 1.68 times Joseph’s distance. Let’s test each value for Joseph’s distance and try to find a suitable value for Alice’s distance.

If Joseph’s distance is 21, then Alice’s distance must be 21 * 1.68 = 35.28, which is not among the answer choices.

If Joseph’s distance is 25, then Alice’s distance must be 25*1.68 = 42, which IS among the answer choices. So, 25 and 42 are possible values for the distances of Joseph and Alice, respectively.

Answer: Joseph - 25, Alice - 42