Two ferryboats leave opposite sides of a lake at the same ti

Two ferryboats leave opposite sides of a lake at the same time. They pass
eachother when they are 800 meters from the nearest shore. When it reaches
the opposite side, each boat spends 30 minutes at the dock and then starts
back. This time the boats pass each other when they are 400 meters from the
nearest shore. Assuming that each of the boats travels at the same speed in
both directions, how wide is the lake between the two ferry docks?

Solution

LET US MARK 2 SHORES AS S1 AND S2 AND THE 2 BOATS AS B1 STARTING FROM
S1 AND B2 STARTING FROM S2
LET SPEED OF FASTER BOAT B1 BE KX WHERE K IS GREATER THAN 1 .
LET THE DISTANCE BETWEEN 2 SHORES BE L