Passing the Ball

Date: 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/