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This problem trains for: Math Kangaroo 5-6, Math Kangaroo 7-8, AMC-8, AMC-10, GMAT.

Exactly after the first 40 days of his journey "around the world in 80 days," Phileas Fogg calculated that he had traveled not half, but only a quarter of the itinerary. He became very alarmed and told Passepartout that they would have to increase their speed by 100% in order to finish the journey on time and win the bet with the Reform Club.

Passepartout, however, said: "Monsieur, I doubt that this increase in speed would be sufficient."

If Passepartout is right, at the new speed, by how much percent would the duration of their journey be longer than the projected 80 days?

(characters from Jules Verne's "Around the World in 80 Days")

Assume the itinerary to have size 100 units. In the first 40 days, Fogg has covered only 25 units of itinerary at a rate of (itinerary/time):

equation

The rate he proposes to travel at from now on is:

equation

The number of journey units he can travel at this rate in the remaining 40 days is:

equation

equation

This is 25 journey units short of the total length of the itinerary.

He can travel 25 journey units in:

equation

days. This is longer than the proposed duration by 25%:

equation

equation