Title: How to Calculate Overall Average Speed for Multi-Leg Car Journeys

Understanding average speed is essential for planning efficient road trips and interpreting vehicle performance. In many driving scenarios, a journey consists of multiple segments traveled at different speeds. A common example is a car that drives 150 miles at 50 mph, followed by 200 miles at 60 mph. But what is the car’s overall average speed for the entire trip? This article breaks down the calculation and explains why average speed isn’t simply the arithmetic mean of the two speeds.

Understanding the Context

The Journey Breakdown

The journey has two distinct segments:

  1. First leg:

    • Distance: 150 miles
    • Speed: 50 mph
    • Time = Distance ÷ Speed = 150 ÷ 50 = 3 hours

  2. Second leg:

    • Distance: 200 miles
    • Speed: 60 mph
    • Time = 200 ÷ 60 = 3.333... hours (or 3 hours 20 minutes)
A car travels 150 miles at an average speed of 50 mph, then another 200 miles at an average speed of 60 mph. What is the car's overall average speed for the entire journey?

Key Insights

Total Distance and Total Time

  • Total distance traveled:
    150 + 200 = 350 miles

  • Total time for the journey:
    3 + 3.333... = 6.333... hours (or 6 hours and 20 minutes)

Continue Reading

Substitute the radius of the outer edge:
C = 2\pi \times 13 = 26\pi
Thus, the circumference of the outer edge of the walking path is \(\boxed{26\pi}\) meters.

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Final Thoughts

Calculating Overall Average Speed

> Average speed = Total distance ÷ Total time

Plugging in the numbers:
350 miles ÷ 6.333... hours ≈ 55.26 mph

Why Average Speed Is NOT the Mean of the Two Speeds

A common mistake is to assume the average speed is (50 + 60) ÷ 2 = 55 mph. However, average speed accounts for time spent at each speed. Since the car spends more time traveling at 50 mph, this pulls the overall average below 55 mph.

The correct approach weights each segment by the time spent, confirming a more accurate overall average speed of roughly 55.26 mph.

Practical Takeaway

When planning long drives or analyzing driving efficiency, always calculate total distance divided by total time. This provides the true picture of how long the trip took, regardless of variable speeds. For the journey covering 350 miles, you’ll spend just over 6 hours — proving the importance of proper averaging in real-world driving scenarios.