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Queation Ava wants to take a train to Pierre. There are two trains that go in that direction. There's a local train, which makes stops along the way and there's an express train, which doesn't make stops along the way. Ava got to the station just as two trains pulled away, one express and one local. If a local train runs every 4 hours and an express train runs every 5 hours, how much longer will it be until the next time two trains leave at the same time? Answer Alumpr a out of a It will be show Examples mours until the next time two trains leave at the same time.

Ask by Santiago Rowe. in the United States
Jan 27,2025

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Both trains will next depart together in 20 hours.

Solución

To determine how much longer it will be until both the local and express trains leave the station at the same time again, we need to find the **Least Common Multiple (LCM)** of their departure intervals. - **Local train:** Departs every **4 hours** - **Express train:** Departs every **5 hours** **Calculating the LCM of 4 and 5:** 1. **List the multiples of each number:** - Multiples of 4: 4, 8, 12, 16, **20**, 24, ... - Multiples of 5: 5, 10, 15, **20**, 25, ... 2. **Identify the smallest common multiple:** - The first common multiple of both 4 and 5 is **20**. **Conclusion:** The next time both trains will depart the station simultaneously is **20 hours** from now. **Answer:** Both trains will next depart together in 20 hours.

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To find out when the next local and express trains will leave at the same time, we can find the least common multiple (LCM) of their frequencies. The local train runs every 4 hours, and the express train runs every 5 hours. The LCM of 4 and 5 is 20, meaning that the next time both trains depart together will be in 20 hours. So, it will be 20 hours until the next time two trains leave at the same time! Train schedules have a rich history! Did you know that the first public railway to use steam locomotives was the Stockton and Darlington Railway in England, established in 1825? This innovation not only revolutionized transport but also set the stage for the global railway network we see today! For those who travel by train often, it can be smart to familiarize yourself with train schedules and app options. Common mistakes include assuming that trains will be on time without checking for delays or changes. Always double-check your schedule, especially if you're connecting to another train or meeting someone at the destination!

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