A piece of work was done by A, B, C; at first A worked alone but after some days was joined by B, and these two after some days were joined by C. The whole work might have been done by B and C if they had each worked twice the number of of days that they actually did. The whole work could also have been completed without B's help if A had worked two thirds and C four times the number of days they actually did; or if A and B had worked together for 40 days without C; or if all together if had worked together for the time that B had worked. The number of days that elapsed before B began to work was to the number that elapsed before B began to work as 3 to 5; find the number of days that A worked.

A:30
B:35
C:45
D:57
E:65