There are two islands X and Y at a distance apart. A ship is moving back and forth between the islands X and Y transporting people and goods. Its back tip B is touching the island Y . The ship will move forward and reach island X exactly in twenty minutes from the time of departure , and its front tip A will touch the island X . There is a runway between the tips A and B on the ship. A man called K , jumps from the island Y on to the ship at the point B of the runway. Immediately the ship starts moving towards the island X . K takes rest for five minutes , and starts to run on the runway, at a uniform speed of forty metres per minute , from the tip B towards the tip A . When the ship reaches the island X , the tip A touches the island X . Exactly by the same time , K reaches the tip A and jumps on to the ground of the island X. There is no break in his run. If the ship always moves at a uniform speed of seven metres per minute , what is the distance between the islands X and Y ?
------------------------------------------------------ Distance between the islands is equal to the distance between X and Y that is XY. At the time of departure of the ship, the rear tip B of the ship is touching the island Y. At that time the distance XY = Length XA plus length AB ( since B and Y are coinciding ). Length XA is covered by the ship in twenty minutes at the rate of seven metres per minute . Hence XA = 20×7 = 140 metres.....( 1 ). In the twenty minutes of travel K takes rest for five minutes and in the remaining fifteen minutes he covers the distance BA ( = the length of the ship , which is also = the length YA , at the time of departure of a ship ) and K jumps on the ground of the island X exactly on reaching the tip A. Hence YA = 15 × 40 =600 metres(2) So the distance between the islands = 140 + 600 = 740 metres.
