# The ring chase

**Algebra**Level 3

Frodo and Gollum are 900 meters apart in an infinitely long, lighted tunnel in Middle-Earth. Frodo has the ring, which makes him invisible. He can wear the ring for 15 seconds until it falls off, and then it takes him 5 seconds to put it back on. Frodo runs at a rate of 8 meters per second away from Gollum, but he cannot run while he puts the ring on. Gollum runs at a rate of 30 meters per second towards Frodo, but Gollum can only run if Frodo doesn't have the ring on. In seconds, how long does it take for Gollum to catch up with Frodo?

Frodo has the ring on to begin with for 15 seconds as normal.

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