CEMC Hypatia, 2010

Algebra Difficulty 2.0 Junior Prove it Canada

Piravena must make a trip from $A$ to $B$ , then from $B$ to $C$ , then from $C$ to $A$ . Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with $C$ a distance of $3000$ km from $A$ and with $B$ a distance of $3250$ km from $A$ . To take a bus, it costs Piravena $0.15 per kilometre. To take an airplane, it costs her a $100 booking fee, plus $0.10 per kilometre. Determine the distance she travels for her complete trip.

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