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
Let the distance covered by Tom be \(Y\) and by Linda be \(X\)
NOTE: In 1 hour Linda has already travelled 2 milesCase 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