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Alice leaves the Malefeco Corporation building and travels due east fo

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Alice leaves the Malefeco Corporation building and travels due east fo  [#permalink]

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New post Updated on: 22 Nov 2019, 09:57
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Question # 53, Date : 22-Nov-2019
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Alice leaves the Malefeco Corporation building and travels due east for 20 minutes, then due south for 30 minutes, then due east for 10 minutes, at a constant rate of speed. Joseph leaves the Malefeco Corporation building and travels due north for 40 minutes, then turns and travels due west for 30 minutes, at a constant rate of speed. Alice's speed is twice Joseph's speed.

Select possible approximate distances from Malefeco for Alice and Joseph at the end of their respective journeys consistent with the information above.

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Originally posted by avi2crackgmat on 03 Mar 2013, 15:07.
Last edited by SajjadAhmad on 22 Nov 2019, 09:57, edited 2 times in total.
Updated - Complete topic (198).
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Re: Alice leaves the Malefeco Corporation building and travels due east fo  [#permalink]

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New post 03 Mar 2013, 15:10
I am particularly confused by the usage of the word "distance" in the question stem as below - looks more of a displacement rather than a distance but I may be thinking too much

Select possible approximate distances from Malefeco for Alice and Joseph at the end of their respective journeys consistent with the information above.
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Re: Alice leaves the Malefeco Corporation building and travels due east fo  [#permalink]

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New post 18 Mar 2013, 09:36
avi2crackgmat wrote:
Alice leaves the Malefeco Corporation building and travels due east for 20 minutes, then due south for 30 minutes, then due east for 10 minutes, at a constant rate of speed. Joseph leaves the Malefeco Corporation building and travels due north for 40 minutes, then turns and travels due west for 30 minutes, at a constant rate of speed. Alice's speed is twice Joseph's speed.

Select possible approximate distances from Malefeco for Alice and Joseph at the end of their respective journeys consistent with the information above.

Alice 42, Joseph 25

In terms of time:
Alice traveled 30 min (east) and 30 min (south)
Joseph traveled 40 min (north) and 30 min (west)

In terms of distance:
If Alice travel at 1 yard/min --> Joseph travel at 0.5 yard/min
Alice traveled 30\sqrt{2} yards (it's a 45-45-90 triangle), which is approximately 42 yards.
Joseph traveled 25 yards (30-60-90 triangle --> 15-20-25 or a 3-4-5 ratio)
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Re: Alice leaves the Malefeco Corporation building and travels due east fo  [#permalink]

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New post 18 Jan 2020, 04:21
ScottTargetTestPrep I understand all of your explanations in your comments. Can you please help break down calculations for this problem?
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Re: Alice leaves the Malefeco Corporation building and travels due east fo  [#permalink]

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New post 28 Jan 2020, 09:53
lacabral wrote:
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
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Re: Alice leaves the Malefeco Corporation building and travels due east fo   [#permalink] 28 Jan 2020, 09:53
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