MathDB

3

Part of 2008 AIME Problems

Problems(2)

Ed and Sue

Source: AIME 2008I Problem 3

3/23/2008
Ed and Sue bike at equal and constant rates. Similarly, they jog at equal and constant rates, and they swim at equal and constant rates. Ed covers 74 74 kilometers after biking for 2 2 hours, jogging for 3 3 hours, and swimming for 4 4 hours, while Sue covers 91 91 kilometers after jogging for 2 2 hours, swimming for 3 3 hours, and biking for 4 4 hours. Their biking, jogging, and swimming rates are all whole numbers of kilometers per hour. Find the sum of the squares of Ed's biking, jogging, and swimming rates.
modular arithmeticcalculusintegrationAMC
Cheese-Cutting

Source: AIME 2008II Problem 3

4/3/2008
A block of cheese in the shape of a rectangular solid measures 10 10 cm by 13 13 cm by 14 14 cm. Ten slices are cut from the cheese. Each slice has a width of 1 1 cm and is cut parallel to one face of the cheese. The individual slices are not necessarily parallel to each other. What is the maximum possible volume in cubic cm of the remaining block of cheese after ten slices have been cut off?
geometry3D geometryAMC