Passing the BallDate: 09/27/97 at 12:32:10 From: MELODIE Subject: Word problems How long would it take to pass a basketball from one person to another in a line 2833 miles from San Francisco to Washington, DC? Thank you. Date: 10/03/97 at 18:30:21 From: Doctor Mike Subject: Re: Word problems Hello Melodie, This is an interesting problem. I can't give a complete answer because of the many different ways you could put together such a line. I'll show you how to do it one way, and then you will know how to do it in other ways, too. You have to know how far apart the people in the line are standing, and how fast they can move the ball from person to person. I think it is reasonable for there to be a person every 3 feet. That is, from the middle of one to the middle of the next is one yard. That puts them close enough to each other, but far enough apart to have a little space in between. I will also assume that a person can give the ball to the next person in 1 second. Because there are 5280 feet in a mile, there are 5280/3 or 1760 yards in a mile. That means that there are 1760 people standing in line every mile. Remember the hand-off time is 1 second, so it takes 1760 seconds for the ball to go one mile. For it to go 2833 miles would take 2833*1760 seconds. That is 4986080 (almost 5 million) seconds. How many hours is that? Let's do some conversions. 4986080 seconds divided by 60, gives 83101.333 minutes. Divide that by 60 again to get 1385.0222 hours. Divide that by 24 to get 57.709259 days. Divide that by 7 to get 8.2441799 weeks. So, that shows you the time in several ways, all of which mean almost 2 months. The answer will be different if the ball actually moves slower or faster in your line than it does in mine. For instance, if the people are standing 15 feet apart so that each person has to really pass it rather than just hand it off, AND if they each can still do one pass per second, then the ball will move 5 times as fast and the whole trip will happen in 1/5 of the time I figured. I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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