Re: Physics of Coffee Cups

[Maurice Barnhill <mvb@UDEL.EDU>]

Oops, I assumed that both transfers were the same size.

Maurice Barnhill wrote:
> This is a new problem for me also, so I looked at it
algebraically.
> No assumptions are needed.  Call the cups 1 (originally coffee)
and 2,
> and the amount of coffee, which is the same as the amount of tea,
N.
> Then after both transfers
>
> 1:  c_1 + t_1 = N
> 2:  c_2 + t_2 - N
>
> However, the total amount of coffee and the total amount of tea is
also
> N, so
>
> 3:  c_1 + c_2 = N
> 4:  t_1 + t_2 = N
>
> (Equation 4 is not independent; it is eq. 1 + eq. 2 - eq. 3 .)
>
> Subtract eq. 3 from eq. 1 and you have
>
> t_1 - c_2 = 0
>
> so the amount of tea in the first cup (t_1) is equal to the amount
of
> coffee in the second cup (c_2).  No information about the transfer
is
> needed.
--
Maurice Barnhill (mvb@udel.edu)
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716