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Tom and Linda stand at point A. Linda begins to walk in a straight
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21 May 2021, 08:13
21 May 2021, 08:13
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Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A. 60
B. 72
C. 84
D. 90
E. 108
A. 60
B. 72
C. 84
D. 90
E. 108
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Tom and Linda stand at point A. Linda begins to walk in a straight
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23 May 2021, 11:04
23 May 2021, 11:04
1
GeminiHeat wrote:
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A. 60
B. 72
C. 84
D. 90
E. 108
A. 60
B. 72
C. 84
D. 90
E. 108
Let the distance covered by Tom be \(Y\) and by Linda be \(X\)
NOTE: In 1 hour Linda has already travelled 2 miles
Case I: Tom covers half of the distance that of Linda
|---- Y ----|--- 2 ---|-- X --|
\(Y = \frac{(2 + X)}{2}\)
Thus,
\(\frac{(2 + X)}{(2)(6)} = \frac{x}{2}\)
\(2x + 4 = 12x\)
\(x = \frac{4}{10} = \frac{2}{5}\)
Distance travelled by Tom = \(\frac{(x + 2)}{2} = \frac{12}{10}\)
Time \(= \frac{12}{(10)(6)} = \frac{2}{10}\) hrs \(= 12\) minutes
Case II: Tom covers twice the distance that of Linda
|---- Y ----|--- 2 ---|-- X --|
\(Y = 2(2 + X)\)
Thus,
\(\frac{2(2 + X)}{6} = \frac{x}{2}\)
\(2x + 4 = 3x\)
\(x = 4\)
Distance travelled by Tom = \(2(x + 2) = 2(4 + 2) = 12\)
Time \(= \frac{12}{6} = 2\) hrs \(= 120\) minutes
Therefore, difference of time = \(120 - 12 = 108\) minutes
Hence, option E
Re: Tom and Linda stand at point A. Linda begins to walk in a straight
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23 Jul 2024, 02:46
23 Jul 2024, 02:46
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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