Jack and Jeremy have been obsessed with Pokémon Go recently. When they were walking around at Pokéstops, they each collected 9 eggs. In order to hatch an egg in Pokémon Go, the egg must be in an egg incubator, and the person must walk a certain distance. Jack has two 2 km eggs, six 5 km eggs, and one 10 km egg. Jeremy has two 2 km eggs, four 5 km eggs, and three 10 km eggs. Jack and Jeremy decide to have a race to see who can hatch their eggs the fastest.
a) Jack and Jeremy start with one egg incubator that has infinite uses, but can only hatch one egg at a time. If Jeremy has an average speed of 9 km/hour, how fast would Jack have to run, on average, in order to tie with Jeremy?
b) Jack decides that he doesn’t want to run, so he decides to be lazy and buy 8 more egg incubators so he can hatch all nine of his eggs at the same time. Jack has 120 Pokécoins, and egg incubators cost 150 Pokécoins each. When Jack goes to the Shop to purchase Pokécoins, he can either buy 100 Pokécoins for $0.99, 550 Pokécoins for $4.99, or 1200 Pokécoins for $9.99. What is the lowest amount of money, in dollars, that Jack could pay to get 8 egg incubators?
c) Jack realizes he only has enough money on his iTunes account to buy one extra egg incubator. If Jack buys a second egg incubator, how quickly would Jack have to walk in order to tie with Jeremy?
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