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