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31 Dec 2023, 06:32
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Two trains, A and B, depart from stations X and Y respectively, and head toward each other. The speed of A is twice that of B. If when they meet, the slower train has traveled 30 km less than the faster train, what is the distance between stations X and Y?
A. 30 km
B. 45 km
C. 60 km
D. 75 km
E. 90 km
A. 30 km
B. 45 km
C. 60 km
D. 75 km
E. 90 km
31 Dec 2023, 06:33
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Official Solution:
Two trains, A and B, depart from stations X and Y respectively, and head toward each other. The speed of A is twice that of B. If when they meet, the slower train has traveled 30 km less than the faster train, what is the distance between stations X and Y?
A. 30 km
B. 45 km
C. 60 km
D. 75 km
E. 90 km
Since the speed of A is twice that of B, then when they meet, A would have covered twice the distance (\(2d\)) that B would have covered (\(d\)). Given that the difference in the distance covered is 30 km, we get:
\(2d - d = 30\);
\(d = 30\) km.
The distance between stations X and Y is the sum of the distances covered by A and B by the time they meet. Hence, the total distance is \(2d + d = 3d = 90\) km.
Answer: E
Two trains, A and B, depart from stations X and Y respectively, and head toward each other. The speed of A is twice that of B. If when they meet, the slower train has traveled 30 km less than the faster train, what is the distance between stations X and Y?
A. 30 km
B. 45 km
C. 60 km
D. 75 km
E. 90 km
Since the speed of A is twice that of B, then when they meet, A would have covered twice the distance (\(2d\)) that B would have covered (\(d\)). Given that the difference in the distance covered is 30 km, we get:
\(2d - d = 30\);
\(d = 30\) km.
The distance between stations X and Y is the sum of the distances covered by A and B by the time they meet. Hence, the total distance is \(2d + d = 3d = 90\) km.
Answer: E
12 Jan 2026, 03:56
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