2004 Fermat Problem 21

Bill and Jill are hired to paint a line on a road. If Bill works by himself, he could paint the line in B hours. If Jill works by herself, she could paint the line in J hours. Bill starts painting the line from one end, and Jill begins painting the line from the other end one hour later. They both work until the line is painted. Which is the following is an expression for the number of hours that Bill works?

\textbf{(A)}\ \frac{B(J+1)}{B+J}\quad \textbf{(B)}\ J+1\quad \textbf{(C)}\ \frac{BJ}{B+J}+1\quad \textbf{(D)}\ \frac{B+J-1}{2}\quad \textbf{(E)}\ \frac{B(J-1)}{B+J}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.