Gandalf's fireworks

Level pending

Gandalf shoots off fireworks at Bilbo's birthday party. The fireworks go off at 100 m/s from the ground. They go up, explode, and then come back down immediately. The moment the fireworks shoot up, Bilbo rushes to his house 50 meters away at a rate of 5 m/s. He takes 1 second to grab the ring and rushes back at a rate of 8 m/s. How long before Gandalf's fireworks come to the ground will Bilbo return to the party with the ring? Express your answer in seconds as a decimal to the nearest hundredth.

The acceleration of gravity is -9.8 m/s^2. Neglect air resistance.

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