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Is the average speed 50mph, if I travel 100 miles at 40mph and 100 miles at 60mph?

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1

$begingroup$

I am a little confused about the average speed of a journey.

If I travel at 40mph for the first 100 miles of the journey and then 60mph for the other 100 miles of the 200 mile journey, then is my average speed of the journey 50mph?

If I use the formula:
$$ textAverage speed = fractextTotal distancetextTotal time,$$

then, I get

$$textAverage speed= frac100+100frac52+frac53 =48textmph.$$

I don’t quite understand why I get different answers?

algebra-precalculus classical-mechanics

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asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Your first method for finding average is incorrect. It is only taking into consideration the data values but completely ignoring the frequency aspect of the data.
  $endgroup$
  – Anurag A
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Average speed is not really the average of the speeds, but their time-weighted average.
  $endgroup$
  – Shubham Johri
  8 hours ago
  
  

  
  
  
  

add a comment | 

1

$begingroup$

I am a little confused about the average speed of a journey.

If I travel at 40mph for the first 100 miles of the journey and then 60mph for the other 100 miles of the 200 mile journey, then is my average speed of the journey 50mph?

If I use the formula:
$$ textAverage speed = fractextTotal distancetextTotal time,$$

then, I get

$$textAverage speed= frac100+100frac52+frac53 =48textmph.$$

I don’t quite understand why I get different answers?

algebra-precalculus classical-mechanics

share|cite|improve this question

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Your first method for finding average is incorrect. It is only taking into consideration the data values but completely ignoring the frequency aspect of the data.
  $endgroup$
  – Anurag A
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Average speed is not really the average of the speeds, but their time-weighted average.
  $endgroup$
  – Shubham Johri
  8 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

I am a little confused about the average speed of a journey.

If I travel at 40mph for the first 100 miles of the journey and then 60mph for the other 100 miles of the 200 mile journey, then is my average speed of the journey 50mph?

If I use the formula:
$$ textAverage speed = fractextTotal distancetextTotal time,$$

then, I get

$$textAverage speed= frac100+100frac52+frac53 =48textmph.$$

I don’t quite understand why I get different answers?

algebra-precalculus classical-mechanics

share|cite|improve this question

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

$endgroup$

share|cite|improve this question

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

share|cite|improve this question

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

asked 8 hours ago

GurjinderGurjinder

61866 silver badges1818 bronze badges

2 Answers
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2

$begingroup$

Here's a thought experiment that may help:

Imagine that you travel the first $100$ miles at $100$ miles per hour and then teleport instantaneously for the second $100$ miles. Then your average speed is clearly $200$ miles per hour (total distance over total time).

What would your method give as an answer?

You can't simply average speeds.

share|cite|improve this answer

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

$endgroup$

add a comment | 

7

$begingroup$

The average is below 50 because you are traveling at the lower speed for a longer period of time

This is why, if you run the 400m on a 400m track, your best option is to have no wind... the advantage you would get from having the wind in your back is less than the disadvantage from running into the wind since you are running into the wind for a longer period

share|cite|improve this answer

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

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add a comment | 

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2

$begingroup$

Here's a thought experiment that may help:

Imagine that you travel the first $100$ miles at $100$ miles per hour and then teleport instantaneously for the second $100$ miles. Then your average speed is clearly $200$ miles per hour (total distance over total time).

What would your method give as an answer?

You can't simply average speeds.

share|cite|improve this answer

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

$endgroup$

add a comment | 

2

$begingroup$

Here's a thought experiment that may help:

Imagine that you travel the first $100$ miles at $100$ miles per hour and then teleport instantaneously for the second $100$ miles. Then your average speed is clearly $200$ miles per hour (total distance over total time).

What would your method give as an answer?

You can't simply average speeds.

share|cite|improve this answer

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

$endgroup$

add a comment | 

$begingroup$

Here's a thought experiment that may help:

Imagine that you travel the first $100$ miles at $100$ miles per hour and then teleport instantaneously for the second $100$ miles. Then your average speed is clearly $200$ miles per hour (total distance over total time).

What would your method give as an answer?

You can't simply average speeds.

share|cite|improve this answer

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

$endgroup$

share|cite|improve this answer

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

answered 7 hours ago

Ethan BolkerEthan Bolker

53.7k55 gold badges6161 silver badges131131 bronze badges

7

$begingroup$

The average is below 50 because you are traveling at the lower speed for a longer period of time

This is why, if you run the 400m on a 400m track, your best option is to have no wind... the advantage you would get from having the wind in your back is less than the disadvantage from running into the wind since you are running into the wind for a longer period

share|cite|improve this answer

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

$endgroup$

add a comment | 

7

$begingroup$

The average is below 50 because you are traveling at the lower speed for a longer period of time

This is why, if you run the 400m on a 400m track, your best option is to have no wind... the advantage you would get from having the wind in your back is less than the disadvantage from running into the wind since you are running into the wind for a longer period

share|cite|improve this answer

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

$endgroup$

add a comment | 

$begingroup$

The average is below 50 because you are traveling at the lower speed for a longer period of time

This is why, if you run the 400m on a 400m track, your best option is to have no wind... the advantage you would get from having the wind in your back is less than the disadvantage from running into the wind since you are running into the wind for a longer period

share|cite|improve this answer

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

$endgroup$

share|cite|improve this answer

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges

answered 8 hours ago

Bram28Bram28

67.4k44 gold badges4848 silver badges9393 bronze badges