sammy04 wrote:
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
When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same.
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.
.
_________________
GMAT and GRE Tutor for over 20 years
Recent success stories for my students:admissions into Booth, Kellogg, HBS, Wharton, Tuck, Fuqua, Emory and others.
Available for live sessions in NYC and remotely all over the world
For more information, please email me at GMATGuruNY at gmail