A fleet of ships is sailing in a column, with a destroyer initially positioned at the end of the column.

The destroyer goes on patrol up the column: it leaves its position at the end of the column and proceeds to the head of the column, then turns around and returns to its former position. The destroyer and the column maintain a steady speed during the manoeuvre When the destroyer regains its position, the Captain notes that the end of the column now occupies the position which the head of the column had occupied when he first left his own position.

Assuming that the time required for the destroyer to get up to speed and also the time required for the destroyer to reverse its direction is zero, determine the ratio of the destroyer’s speed to that of the main column during its patrol.