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Lakes And Boats Riddle

There is a lake with shores A and B. Two motorboats M and N are standing on the opposite sides (A and B respectively). M leaves A and N leaves B and start moving with constant speeds. They meet for the first time 500 yards away from A. After touching the shores, they return back to the previous shore point without taking any break. This time they meet at 300 yards away from B.

Can you determine how wide the lake is? What is the relation between the speeds of boats?
When the boats meet for the first time, they have sailed a combined distance that is equal to one length of the lake. When they meet the second time, they have sailed 3 lengths. The elapsed time and the distance for each is three times.

When they meet for the second time, the boat M has sailed 500 x 3 = 1500 yards. Now, this is 300 yards longer than the length of the lake, it must be 1200 yards wide.

The ration between the speed of boat M and boat N is equal to the ratio of the distance that they have sailed before they meet the first time.
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