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30 May 2026, 10:04
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Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?
(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
(2) Bus R traveled 3 times as fast as Bus S.
(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
(2) Bus R traveled 3 times as fast as Bus S.
30 May 2026, 10:04
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Official Solution:
Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?
(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
Let the distance between the depot and Central Square station be \(D\) kilometers. So, this tells us that Bus S had traveled \(D - 250\) kilometers. We do not know anything else. Not sufficient.
(2) Bus R traveled 3 times as fast as Bus S.
This gives only the ratio of their speeds. Not sufficient.
(1)+(2) From (1), when the buses met, Bus S had traveled \(D - 250\) kilometers. Since Bus R traveled 3 times as fast as Bus S, in the same time Bus R had traveled \(3(D - 250)\) kilometers.
But Bus R had gone from the depot to Central Square station and then back 250 kilometers, so Bus R had traveled \(D + 250\) kilometers. Therefore:
\(3(D - 250) = D + 250\)
\(D = 500\)
Sufficient.
Answer: C
Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?
(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
Let the distance between the depot and Central Square station be \(D\) kilometers. So, this tells us that Bus S had traveled \(D - 250\) kilometers. We do not know anything else. Not sufficient.
(2) Bus R traveled 3 times as fast as Bus S.
This gives only the ratio of their speeds. Not sufficient.
(1)+(2) From (1), when the buses met, Bus S had traveled \(D - 250\) kilometers. Since Bus R traveled 3 times as fast as Bus S, in the same time Bus R had traveled \(3(D - 250)\) kilometers.
But Bus R had gone from the depot to Central Square station and then back 250 kilometers, so Bus R had traveled \(D + 250\) kilometers. Therefore:
\(3(D - 250) = D + 250\)
\(D = 500\)
Sufficient.
Answer: C
