I have a rope and I cut it into two different integer lengths and gave one of them to Alice, the other one to Bob. Then I asked Alice and Bob to cut their ropes into pieces in such a way that when they multiply the length of their own rope pieces, the result shall be the maximum. Both did it right and got their pieces of ropes!
It is known that Bob's original rope length was six times than Alice's and the number of rope pieces that Bob obtained is five times the number that Alice had.
What is the original length of the rope?
- They cut their own robe at least once.
- The length of the pieces is not neccessarily integer values.