During an exercise a column of soldiers were marching at a constant speed. At the end of the column was a messenger. He was commanded to proceed to the head of the column, deliver a dispatch and return to his former position at the back of the column, without delay.
On regaining his former position he noticed that the end of the column was in the same position that the head of the column had occupied when he first left his own position.
What is the ratio of the messenger's speed to that of the column whilst this order was being carried out? (Assume that no time was wasted in delivering the message or returning to his former position.)