The distance between stations P and Q is "D" km
Let speed of passenger train and goods train are 5s km/h and 3s km/h, respectively.
Let length passenger train and goods train are L meters and M meters, respectively.
From I:
D/(5s - 3s) = 5
=> D = 5 * 2s
=> D = 10s ---(1)
But from this data we can not answer the question.
From II:
(L + 440)/(5s * 5/18) = 48
=> L + 440 = 5s * 5/18 * 48
=> L + 440 = 200s/3 ---(2)
And (M + 460)/[(3s + 55) * 5/18] = 28.8
=> M + 460 = (3s + 55) * 28.8 * 5/18
=> M + 460 = 8(3s + 55) ---(3)
From this data we cannot answer the following question.
From III:
L + M = 900 ---(4)
And D/(5s + 3s) = 5/4
=> D = 5/4 * 8s
=> D = 10s ---(5)
From this data we cannot answer the following question.
From I and II together:
=> D = 10s ---(1)
=> L + 440 = 200s/3 ---(2)
=> M + 460 = 8(3s + 55) ---(3)
By combining statements I and II, we cannot find the answer.
From II and III together:
Adding equation (2), and (3), we get
L + 440 + + M + 460 = 200s/3 + 8(3s + 55)
=> L + M + 900 = 272s/3 + 440
=> 900 + 900 - 440 = 272s/3
=> 1360 * 3/272 = s
=> s = 15
Hence, D = 10 * 15 = 150 km
Therefore, statement II and III together are sufficient to answer the question.
From I and III together:
=> D = 10s ---(1)
L + M = 900 ---(4)
=> D = 10s ---(5)
Combining equation (1), (4), and (5), we cannot answer the question.
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