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An inspection cart travels from a main workshop to a remote monitoring station and then returns to the workshop along the same track. On the trip to the monitoring station, the cart travels at a constant speed of 45 kilometers per hour. If the return trip takes 6 hours, how many hours does the cart take to reach the monitoring station?
(1) The distance from the workshop to the monitoring station is 180 kilometers.
(2) The cart’s average (arithmetic mean) speed for the entire round trip is 36 kilometers per hour.
(1) The distance from the workshop to the monitoring station is 180 kilometers.
(2) The cart’s average (arithmetic mean) speed for the entire round trip is 36 kilometers per hour.
13 Jan 2026, 10:27
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Official Solution:
An inspection cart travels from a main workshop to a remote monitoring station and then returns to the workshop along the same track. On the trip to the monitoring station, the cart travels at a constant speed of 45 kilometers per hour. If the return trip takes 6 hours, how many hours does the cart take to reach the monitoring station?
(1) The distance from the workshop to the monitoring station is 180 kilometers.
If the one way distance is 180 kilometers and the speed on the first leg is 45 kilometers per hour, then the first leg time is \(\frac{180}{45} = 4\) hours. Sufficient.
(2) The cart’s average (arithmetic mean) speed for the entire round trip is 36 kilometers per hour.
Let the time to reach the monitoring station be \(t\) hours. The distance one way is \(45t\) kilometers. The total round trip distance is \(90t\) kilometers. The total time for the round trip is \(t + 6\) hours. Average speed is total distance divided by total time, so \(\frac{90t}{t + 6} = 36\). Solving gives \(t = 4\). Sufficient.
Answer: D
An inspection cart travels from a main workshop to a remote monitoring station and then returns to the workshop along the same track. On the trip to the monitoring station, the cart travels at a constant speed of 45 kilometers per hour. If the return trip takes 6 hours, how many hours does the cart take to reach the monitoring station?
(1) The distance from the workshop to the monitoring station is 180 kilometers.
If the one way distance is 180 kilometers and the speed on the first leg is 45 kilometers per hour, then the first leg time is \(\frac{180}{45} = 4\) hours. Sufficient.
(2) The cart’s average (arithmetic mean) speed for the entire round trip is 36 kilometers per hour.
Let the time to reach the monitoring station be \(t\) hours. The distance one way is \(45t\) kilometers. The total round trip distance is \(90t\) kilometers. The total time for the round trip is \(t + 6\) hours. Average speed is total distance divided by total time, so \(\frac{90t}{t + 6} = 36\). Solving gives \(t = 4\). Sufficient.
Answer: D
