Title: How Far Does a Train Travel in 8 Hours? Calculating Speed and Distance

When faced with a question like “A train travels 150 miles in 3 hours. If it continues at the same speed, how far will it travel in 8 hours?”, it’s a classic problem in motion calculations. Understanding how to determine speed and project travel distance is not only useful for everyday problem-solving but also essential in fields like transportation, logistics, and mathematics.

Step 1: Calculate the Train’s Speed

Understanding the Context

Speed is defined as the distance traveled divided by the time taken. Using the given information:

  • Distance = 150 miles
  • Time = 3 hours

Speed = Distance ÷ Time = 150 miles ÷ 3 hours = 50 miles per hour (mph)

This means the train moves at a steady speed of 50 mph.

Question:** A train travels 150 miles in 3 hours. If it continues at the same speed, how far will it travel in 8 hours?

Key Insights

Step 2: Predict Distance Over 8 Hours

Now that we know the speed, predicting how far the train travels in 8 hours is simple:

Distance = Speed × Time
Distance = 50 mph × 8 hours = 400 miles

Why This Calculation Matters

Knowing how to extrapolate distance based on speed and time is vital. Railroads rely on precise calculations to schedule departures, estimate arrival times, and optimize fuel usage. Similarly, in everyday life, this type of math helps plan trips, budget travel times, or understand journey planning.

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したがって、直線 \(y = 2x + 3\) 上の点 \((1, 2)\) に最も近い点は \(\left(-\frac{1}{5}, \frac{13}{5}\right)\) です。答えは \(\boxed{\left(-\frac{1}{5}, \frac{13}{5}\right)}\) です。
問題: 関数 \(f(x) = 4x^2 + 12x + 9\) の最小値を求めよ。
解: 関数 \(f(x) = 4x^2 + 12x + 9\) の最小値を見つけるために、まず平方完成を行います。この関数は上に開く二次式です（\(x^2\) の係数が正であるため）。

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Final Thoughts

Final Answer:
If a train travels 150 miles in 3 hours at a constant speed, it will travel 400 miles in 8 hours.

Keywords: train travel, speed calculation, distance formula, how far does a train go, train speed problem, 3-hour journey, 8-hour distance, math problem solution, practical math tip

Meta Description:
Struggling to calculate how far a train travels over time? Learn how to use speed and time to find distance with a simple formula. Find out the train travels 400 miles in 8 hours if it moves at 50 mph.
Tags: train speed, distance over time, math problem, transportation math, speed and time, travel planning