GMATGuruNY wrote:
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.
.
Dear
GMATGuruNYI had the same result but based on the time is reciprocal with speed.
Let T= time to meeting point, VA=speed of A, VB = speed of B
VA/VB = 90/40 = 3x/2xTotal distance = VA*T + VB *T = 5x * T...........1
But
Total distance = VA (T+40) = 3x * T + 120x.......2
By equating 1& 2
5x * T = 3x * T + 120x............cancel x
5 * T = 3 * T + 120
2T = 120......T =60 minutes
Then, A will take 1 hour & 40 minutes to reach its distance.
Is my assumption highlighted valid? or is coincidence in this question?
Thanks in advance