Two boats start towards each other, from the two points exactly opposite of each other on the opposite banks of a river, simultaneously. They meet at a distance of 410 m from one of the banks and continue sailing further till they reach the opposite banks. They take rest for 1 hr each and start off the return journey taking the same route. Now they meet at a distance of 230 m from the same bank. Find the distance between the two banks. (Assume that river water is still.)

The distance between the two banks is = 3(410) - 230 = 1000 m.

Just observe that the moment the two boats meet for the first time, sum of distance travelled by the two boats is d {if I assume the distance between two banks to be d'}.

Now next time when they meet, sum of the distance travelled by the two boats together becomes 3d as both boats have reached to the opposite ends (i.e. travelled a distance of d individually) and then turned back to meet at a point.

Clearly the ratio of time taken to meet for the first time and that to meet for second time is in the ratio of distances travelled i.e. 1 : 3. Also the distances travelled by any individual boat is also in the same ratio 1 : 3 as they also have travelled the distances for same time.

So the boat which had travelled 410m till first meeting, has travelled (d + 230)m for the second meeting. And that\'s how we get the above value for d.