2012-I-10

$\begin{array}{rcl}{\displaystyle \frac{x+y+19+20}{4}}& =& 18\\ x+y& =& 33\end{array}$

In order to have the same median found in (a), $x$ and $y$ must be both smaller than or equal to $16$. Therefore, the maximum value of the sum of $x$ and $y$ is $32$.

However, the sum of $x$ and $y$ must be $33$ in order to have the mean $18\text{ hours}$. Therefore, it is impossible that the new median is the same as the median found in (a).