Time for a child to ask "Are we there yet?"

I was asked by Rebecca Wallace representing Skoda Auto if I could formulate an equation for the time for a child to ask The Question

``Are we there yet?''

She was interested in the dependence on the number of activities and the number of children in the car, as well as the length of the journey. I agreed to help as a fun exercise for people to think about as they set off on holiday with their children.

My best guess for the simplest reasonable equation involving these quantities is

\fbox{\parbox{2.5in}{\begin{equation}T = t_0 + \frac{1 + \beta A}{\alpha C^2} \nonumber\end{equation}}}


Why this form?

Note that the equation contains the fact that if there are no children in the car (C=0) then the time goes to infinity. This is correct since if there are no children in the car then one assumes that nobody will ask ``Are we there yet?''.


This is meant to be fun and to help people think about mathematics. I do not expect the equation to be able to make accurate predictions for your particular children.

* The actual number of interactions between C children is C (C-1)/2 .

Dwight Barkley 2006-07-25