01-24-2007, 10:35 PM
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OK, Tom is at 20K dropping 10/sec. Bill at 2K rising 2/sec.
So the position of Tom at an arbitrary time t is T(t) = 20K - 10t and the Position of Bill at t, B(t) = 2K + 2t.
So they meet when T(t) = B(t) or when 20K-10t = 2K +2t. Therefore 18K = 12t. 18000/12 = t = 1500 seconds.
Then go back and check.
2000 + 2(1500) = 5000
20000 - 10(1500) = 5000
If you plot it out on graph paper, with your y axis in thousands of feet and your x axis in hundreds of seconds, Tom's line starts at (0,20) and drops at a 45 degree angle toward (20,0), Bill's line starts at (0,2) and rises to (15,5) where it meets Tom's line.
Quack Ergo Duck.
Here's another one for you. Hotdogs come in packs of 8. Buns come in Packs of 10. On average, people eat 1 2/3 hotdogs at a sitting. What's the smallest number of people, packs of hotdogs, and packs of buns greater than zero do you need to bring together for no leftovers.
Or Jerry (who was a racecar driver) and Mario (a plumber) take of from Duluth in a sports car and a tow truck respectively. Jerry has enough gas to get him 500 miles (and no way to get more), and averages 80 mph. Mario averages 60 in his tow truck when he's not pulling a car, and 50 when he is, and can get 300 miles without regassing. It takes him 10 minutes to gas up for $80 and 20 to hitch up a car. Austin is 1500 miles. How long until he and Jerry pull into the Western Union in Austin, How long does Jerry sit by the side of the road waiting for Mario to come pick him up, and How much does Mario charge Jerry for the tow to make a 10% profit on gas.
Scratch the last one - I just realized there was some trig involved.