Problem:
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 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?
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Solution:
At the rate of 4 miles per hour, Steve can row a mile in 15 minutes. During that time gallons of water will enter the boat. LeRoy must bail gallons of water during that time. So he must bail at the rate of at least gallons per minute.
OR
Steve must row for 15 minutes to reach the shore, so the amount of water in the boat can increase by at most gallons per minute. Therefore LeRoy must bail out at least gallons per minute.
The problems on this page are the property of the MAA's American Mathematics Competitions