Ask Me Help Desk - Averaging speeds

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Averaging speeds

Suppose that you have a goal of driving two miles at an average rate of 60 mph. During the first mile you drive 30 miles an hour. How fast do you have to drive the second hour to maintain the 60 mph average?

If $x_{1}$ and $x_{2}$ are the distances covered at velocities $v_{1}$ and $v_{2}$ , then the average velocity over the whole trip is

$v=\frac{x_{1}+x_{2}}{\frac{x_{1}}{v_{1}}+\frac{x_{ 2}}{v_{2}}}$

In this case, you are given

$x_{1}=x_{2}=1$ ,

$v_{1}=30$ , and the final being v=60.

So, $v=\frac{1+1}{\frac{1}{30}+\frac{1}{v_{2}}}=60$

The thing is, $v\to {60}$ as $v_{2}\to {\infty}$

Comment on galactus's post

So are you saying that it is an infinite solution, or that it is 60 mph?

In order to achieve 60 mph, you must travel at infinite velocity.

Warp 10. :)

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