Why Is the Average Speed Not Simply the Arithmetic Mean of Two Speeds?

[marco101]

I just wanted to know how to find average speed without knowing the distance. I know average speed is defined as total distance / change in time but what would you do
a person travels to a friend's house and when he is halfway there, he figures out that he has been averaging 30 mph. He drives the last half of the trip at 60 mph.
What is Joe’s average speed for the entire journey?

I figured it was just 30 + 60 divided by 2 but apparently i am wrong. anyone can help?

 

[n1person]

It is not quite that linear because you cover more per time going 60 miles per hour than 30 miles per hour.

We will use dimensional analysis just to make sure our operations are making sense.

60 (m/h) * x (h) + y (m/h) * x (h) = c miles

we also know that 30 (m/h) = c (m) / 2x (h)

so 2x (h) = c (m) / 30 (m/h)

So now you can solve for x, the c's will cancel out (cause it doesn't depend on the distance traveled), solve then for y, and you'll get the answer.