Bill and Jill are hired to paint a line on the 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. Find the expression for the number of hours that Bill works.
The Attempt at a Solution
One hour work of Bill and Jill= 1/B and 1/J respectively.
Time taken by both, if both start working simultaneously= BJ/(B+J) ......(i)
As Jill starts work an hour later, work still left= 1/J
Time taken by Bill to complete the remaining work=(1/J)/(1/B)=B/J ........(ii)
Total time for which Bill had to work= (B(J^2+J+B))/(J(B+J)) ...........(i)+(ii)
But my answer doent match th given options, where is the mistake?