Pregunta
- Trains from the green line and red line set off from the terminal
at the same time at 5 a.m. in the morning. Trains from the green
line set off every 5 minutes and trains from the red line set off
every 6 minutes. What time will trains next set off from both
terminals at the same time?
at the same time at 5 a.m. in the morning. Trains from the green
line set off every 5 minutes and trains from the red line set off
every 6 minutes. What time will trains next set off from both
terminals at the same time?
Ask by Newton Gibbs. in Australia
Mar 28,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The next time both trains will set off from their terminals at the same time is 5:30 a.m. (Option B).
Solución
The green line trains set off every 5 minutes, and the red line trains set off every 6 minutes. We need to find the least common multiple (LCM) of these two intervals to determine when both trains will next set off at the same time.
To find the LCM of 5 and 6, we can list the multiples of each number or use the prime factorization method. The multiples of 5 are 5, 10, 15, 20, 25, 30, … and the multiples of 6 are 6, 12, 18, 24, 30, … The smallest common multiple is 30.
Since the trains set off at 5:00 a.m., we add 30 minutes to this time. Thus, the next time both trains will set off together is at 5:30 a.m.
To find the LCM of 5 and 6, we can list the multiples of each number or use the prime factorization method. The multiples of 5 are 5, 10, 15, 20, 25, 30, … and the multiples of 6 are 6, 12, 18, 24, 30, … The smallest common multiple is 30.
Since the trains set off at 5:00 a.m., we add 30 minutes to this time. Thus, the next time both trains will set off together is at 5:30 a.m.
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Simplifique esta solución Mind Expander
To find the next time both the trains set off together, we need to determine the least common multiple (LCM) of the time intervals. The green line trains leave every 5 minutes, and the red line trains leave every 6 minutes. The LCM of 5 and 6 is 30 minutes. Since both trains start at 5 a.m., they will next set off together at 5:30 a.m.
Imagine the scene at the terminal as both trains gather their passengers, ready to pull away into the dawn. The excitement of people catching early rides will brew as the clock ticks towards 5:30 a.m., when both lines will hum in unison once more!
For a little more fun, consider this: if you happen to be on one of those trains, think about how many stops you’d pass through by 5:30 a.m. if you take the green line. Which station do you think would be your favorite? Perfect for daydreaming on your daily commute!
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