Source: Veritas Prep
A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes
The OA is D
A and B start from Opladen and Cologne respectively at the
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When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same.BTGmoderatorLU wrote:Source: Veritas Prep
A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes
If A takes 1/2 as long as B to travel 10 miles, then A will take 1/2 as long as B to travel 1000 miles.
If A takes 3 times as long as B to travel 500 miles, then A will take three times as long as B to travel 2 miles.
Let M = the meeting point.
Let t = the time for A and B each to travel to M.
Train A:
O ----- t -----> M ----> 40 -----> C
Train B:
O <---- 90 ----M <----- t ------- C
Since A takes t minutes to travel the blue portion, while B takes 90 minutes, the time ratio for A and B to travel the blue portion = t/90.
Since A takes 40 minutes to travel the red portion, while B takes t minutes, the time ratio for A and B to travel the red portion = 40/t.
Since the time ratio in each case must be the same, we get:
t/90 = 40/t
t² = 3600
t = 60.
Thus:
A's total time = t+40 = 60+40 = 100 minutes = 1 hour 40 minutes.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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