MathDB

11

Part of 2008 AMC 10

Problems(2)

Steve and LeRoy's Leaky Boat

Source: AMC 12 2008A Problem 7

2/17/2008
While Steve and LeRoy are fishing 1 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 10 gallons per minute. The boat will sink if it takes in more than 30 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking? <spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 6 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 10
AMC
Recursive Sequence

Source: AMC 10 2008B Problem 11

3/1/2008
Suppose that (un) \left(u_n\right) is a sequence of real numbers satisfying u_{n \plus{} 2} \equal{} 2u_{n \plus{} 1} \plus{} u_{n}, and that u_3 \equal{} 9 and u_6 \equal{} 128. What is u5 u_5? <spanclass=′latex−bold′>(A)</span> 40<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 68<spanclass=′latex−bold′>(D)</span> 88<spanclass=′latex−bold′>(E)</span> 104 <span class='latex-bold'>(A)</span>\ 40 \qquad <span class='latex-bold'>(B)</span>\ 53 \qquad <span class='latex-bold'>(C)</span>\ 68 \qquad <span class='latex-bold'>(D)</span>\ 88 \qquad <span class='latex-bold'>(E)</span>\ 104
AMC