carpedeim wrote:
Two trains A and B start from two points P1 and P2 respectively at the same time and travel towards each other. The difference between their speed is 10 kmph and train A takes one hour more to cover the distance between P1 and P2 as compared to train B. Also by the time they meet, train B has covered 200/9 km more as compared to train A. What is the distance between P1 and P2?
A) 150
B) 200
C) 250
D) 300
E) Data insufficient
Solution:We can let r = the speed of train A; thus, r + 10 = the speed of train B (notice that train A is the slower train). We can let t = the time it takes train A to cover the distance between P1 and P2, so t - 1 = the time it takes train B to cover the same distance. Finally, we can let m = the time it takes for the two trains to meet. We can create the equations:
rt = (r + 10)(t - 1) = (r + r + 10)m
and
(r + 10)m - rm = 200/9
Notice that the first equation is just different ways to express the distance between P1 and P2 and the second second equation expresses the difference in distance traveled between the two trains when they meet. Anyway, solving the second equation, we have:
rm + 10m - rm = 200/9
10m = 200/9
m = 20/9
Solving the left part and the middle part of the first equation, we have:
rt = rt - r + 10t - 10
r + 10 = 10t
(r + 10)/10 = t
r/10 + 1 = t
Solving the left part and the right part of the first equation, we have:
rt = (r + r + 10)m
Substituting m = 20/9 and t = r/10 + 1 into the above equation, we have:
r(r/10 + 1) = (2r + 10)(20/9)
r^2/10 + r = 40r/9 + 200/9
Multiplying the equation by 90, we have:
9r^2 + 90r = 400r + 2000
9r^2 - 310r - 2000 = 0
(r - 40)(9r + 50)
r = 40 or r = -50/9
Since r can’t be negative, r = 40. Since t = r/10 + 1, t = 40/10 + 1 = 5. Since the distance between P1 and P2 is rt, the distance is 40(5) = 200.
Answer: B
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