Calculate Average Speed from Multiple Journeys: 0-100 km/h Data Set

Average Speed with Multiple Journey Segments

What is the average speed according to the data?

TravelTimekm/hDistance3122.570400100210400250

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1

Understand the problem

What is the average speed according to the data?

TravelTimekm/hDistance3122.570400100210400250

2

Step-by-step solution

Let's first remind ourselves of the formula for finding velocity:

V=xt V=\frac{x}{t}

x x = distance
t t = time
V V = velocity

Then substitute the data into the formula:

V=210+40+0+2503+1+2+2.5 V=\frac{210+40+0+250}{3+1+2+2.5}

Calculate accordingly to get:

V=5008.5=58.82 V=\frac{500}{8.5}=58.82

Therefore, the average velocity is 58.82.

3

Final Answer

58.82....

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average speed equals total distance divided by total time
  • Technique: Add all distances (210+40+0+250=500) and all times (3+1+2+2.5=8.5)
  • Check: Verify units match and calculation: 500÷8.5=58.82 km/h ✓

Common Mistakes

Avoid these frequent errors
  • Averaging the individual speeds instead of using total distance/time
    Don't calculate (70+40+0+100)÷4 = 52.5! This gives the wrong answer because different journey segments have different time durations. Always use total distance divided by total time for true average speed.

Practice Quiz

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What is the average speed according to the data?

TravelTimekm/hDistance3122.570400100210400250

FAQ

Everything you need to know about this question

Why can't I just average the speeds 70, 40, 0, and 100?

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Because each journey segment lasted a different amount of time! The 70 km/h journey took 3 hours, while the 40 km/h journey only took 1 hour. Simply averaging speeds ignores these time differences.

What does the 0 km/h represent in this problem?

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The 0 km/h means the person was stationary (not moving) for 2 hours. This could represent a rest stop, traffic jam, or break during the journey.

How do I handle the zero speed when calculating?

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Include it normally! Zero speed for 2 hours means zero distance covered in that time. It still counts as part of the total time: 0 km ÷ 2 hours = 0 km/h.

Why is my answer 58.82 and not a round number?

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Real-world average speeds are often decimal numbers! When you divide 500 by 8.5, you get 58.82... This is the exact mathematical result.

Can I verify this answer makes sense?

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Yes! Check if 58.82×8.5=500 58.82 \times 8.5 = 500 . Also, notice the average speed (58.82) falls between the individual speeds, which makes sense given the time weightings.

What if some journey segments have the same time duration?

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The same method applies! Always use total distance ÷ total time. When time durations are equal, this method naturally gives more weight to longer distances.

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