IBM Ponder This #038 · June 2001

(Based on a puzzle of the nineteenth century by George Lilley, brought to our attention by Amit Elazari.)

This month we once again find a goblin chasing us.

This time we are on a train, heading due east at 60 kilometers per hour.

The goblin starts out 30 kilometers due north of us.
He runs at a constant speed, but (fortunately for us) has lost the ability to plan ahead; he always heads directly towards our current position.

(A clever goblin would aim in front of us, since our train's future motion is so predictable; but our goblin is not clever.) He catches up to us after we have travelled 100 kilometers (that is, after 100 minutes).

How fast does the goblin move?

Solution

Best opened after a real attempt

To be added.