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30 May 2026, 08:23
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Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is \(\frac{2}{5}\) of the speed of the bus that leaves Westhaven.
(2) The two buses pass each other 5 hours after they depart.
(1) The speed of the bus that leaves Eastgate is \(\frac{2}{5}\) of the speed of the bus that leaves Westhaven.
(2) The two buses pass each other 5 hours after they depart.
30 May 2026, 08:23
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Official Solution:
Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is \(\frac{2}{5}\) of the speed of the bus that leaves Westhaven.
A speed ratio alone does not determine the travel time because the distance between Eastgate and Westhaven is unknown. Not sufficient.
(2) The two buses pass each other 5 hours after they depart.
Knowing only when they pass each other does not determine the full travel time because the buses’ speeds are unknown. Not sufficient.
(1)+(2) Let the Westhaven bus’s speed be \(v\). Then the Eastgate bus’s speed is \(\frac{2}{5}v\). In 5 hours, the Westhaven bus travels \(5v\) and the Eastgate bus travels \(5 * \frac{2}{5}v = 2v\). Since they meet after 5 hours, the total distance is \(5v + 2v = 7v\). The Westhaven bus needs to travel that full distance at speed \(v\), so its travel time is \(\frac{7v}{v} = 7\) hours. Sufficient.
Answer: C
Two buses travel on the same highway between Eastgate and Westhaven in opposite directions. Each bus travels at a constant speed. At the same time, one bus leaves Eastgate for Westhaven and the other leaves Westhaven for Eastgate. How many hours does the bus that leaves Westhaven take to reach Eastgate?
(1) The speed of the bus that leaves Eastgate is \(\frac{2}{5}\) of the speed of the bus that leaves Westhaven.
A speed ratio alone does not determine the travel time because the distance between Eastgate and Westhaven is unknown. Not sufficient.
(2) The two buses pass each other 5 hours after they depart.
Knowing only when they pass each other does not determine the full travel time because the buses’ speeds are unknown. Not sufficient.
(1)+(2) Let the Westhaven bus’s speed be \(v\). Then the Eastgate bus’s speed is \(\frac{2}{5}v\). In 5 hours, the Westhaven bus travels \(5v\) and the Eastgate bus travels \(5 * \frac{2}{5}v = 2v\). Since they meet after 5 hours, the total distance is \(5v + 2v = 7v\). The Westhaven bus needs to travel that full distance at speed \(v\), so its travel time is \(\frac{7v}{v} = 7\) hours. Sufficient.
Answer: C
