TUYMAADA 1994 Problem 6

In three houses $A,B$ and $C$ , forming a right triangle with the legs $AC=30$ and $CB=40$ , live three beetles $a,b$ and $c$ , capable of moving at speeds of $2, 3$ and $4$ , respectively. Suppose that you simultaneously release these bugs from point $M$ and mark the time after which beetles reach their homes. Find on the plane such a point $M$ , where is the last time to reach the house a bug would be minimal.