MathDB

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.

Problem Statement