A train travels 150 miles at a speed of 50 miles per hour and then 200 miles at 80 miles per hour. What is the average speed for the entire journey?

Total Average Speed: Calculating the Journey of a 150-Mile Segment at 50 mph Followed by 200 Miles at 80 mph

When traveling long distances, understanding both speed and time is essential—not only for navigation but also to calculate average speeds accurately. A common question that arises is: What is the average speed for a train journey covering 150 miles at 50 miles per hour followed by 200 miles at 80 miles per hour?

In this SEO-optimized article, we break down the journey step by step to determine the overall average speed, an essential metric for planning efficient travel.

Understanding the Context

Understanding the Journey Breakdown

The train travels two consecutive segments:

Segment 1: 150 miles at 50 mph
Segment 2: 200 miles at 80 mph

A train travels 150 miles at a speed of 50 miles per hour and then 200 miles at 80 miles per hour. What is the average speed for the entire journey?

Key Insights

While total distance is straightforward, average speed is defined as total distance divided by total time, not the simple arithmetic mean of speeds.

Step 1: Calculate Time Taken for Each Segment

To find the total time, use the formula:
Time = Distance ÷ Speed

Time for first segment:
150 miles ÷ 50 mph = 3 hours
Time for second segment:
200 miles ÷ 80 mph = 2.5 hours

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Final Thoughts

Total travel time = 3 + 2.5 = 5.5 hours

Step 2: Calculate Total Distance Traveled

Total distance = 150 miles + 200 miles = 350 miles

Step 3: Calculate Average Speed for the Entire Journey

Average Speed = Total Distance ÷ Total Time
= 350 miles ÷ 5.5 hours
≈ 63.64 miles per hour

Final Answer: Average Speed of the Entire Trip

The average speed for the train journey covering 150 miles at 50 mph followed by 200 miles at 80 mph is approximately 63.6 mph, or rounded, 64 mph depending on context.