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05 Jun 2024, 15:11
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A train traveled a certain route that consisted of 3 segments. The second segment lasted twice as long as the first one and the third segment lasted twice as long as the second one. If the average speeds of the train in these segments were 60 km/h, 75 km/h, 35 km/h, what was the average speed of the train, in km/h, over the entire route?
A. 40
B. 50
C. 60
D. 70
E. 80
A. 40
B. 50
C. 60
D. 70
E. 80
05 Jun 2024, 15:11
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Official Solution:
A train traveled a certain route that consisted of 3 segments. The second segment lasted twice as long as the first one and the third segment lasted twice as long as the second one. If the average speeds of the train in these segments were 60 km/h, 75 km/h, 35 km/h, what was the average speed of the train, in km/h, over the entire route?
A. 40
B. 50
C. 60
D. 70
E. 80
Let's assume the time spent on the first segment was \(t\) hours, \(2t\) hours on the second, and \(4t\) hours on the third. The entire journey lasted \(t + 2t + 4t = 7t\) hours. The distances for the segments are \(60t\) km, \(75 * 2t = 150t\) km, and \(35 * 4t = 140t\) km, respectively. Thus, the average speed over the entire route would be \(\frac{\text{total distance}}{\text{total time}} = \frac{60t + 150t + 140t}{7t} = 50\) km/h.
Answer: B
A train traveled a certain route that consisted of 3 segments. The second segment lasted twice as long as the first one and the third segment lasted twice as long as the second one. If the average speeds of the train in these segments were 60 km/h, 75 km/h, 35 km/h, what was the average speed of the train, in km/h, over the entire route?
A. 40
B. 50
C. 60
D. 70
E. 80
Let's assume the time spent on the first segment was \(t\) hours, \(2t\) hours on the second, and \(4t\) hours on the third. The entire journey lasted \(t + 2t + 4t = 7t\) hours. The distances for the segments are \(60t\) km, \(75 * 2t = 150t\) km, and \(35 * 4t = 140t\) km, respectively. Thus, the average speed over the entire route would be \(\frac{\text{total distance}}{\text{total time}} = \frac{60t + 150t + 140t}{7t} = 50\) km/h.
Answer: B
09 Dec 2025, 10:09
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I did not quite understand the solution. The question says the journey lasts and it does specify or clear that if it is distance or time.
