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Snails Crossing the Lawn


Date: 07/26/97 at 10:47:15
From: Philip Carter
Subject: Snails

Can you supply the answer to the following, please ?

It takes 10 snails 50 minutes to cross a lawn from when the first 
snail slithers on to the lawn to the moment the last snail leaves. 
The snails cross in single file and the lawn is only wide enough to 
accommodate 8 snails at any one time. All snails travel at the same 
speed and are on the lawn for the same length of time. For how long is 
that ?
 
Philip Carter


Date: 07/29/97 at 08:32:49
From: Doctor Rob
Subject: Re: Snails

I would make a space-time diagram.

space
^                          1  2  3  4  5  6  7  8  9 10 
|-  -  -  -  -  -  -  -  -/ -/ -/ -/ -/ -/ -/ -/ -/ -/ -  - width of 
|                       /  /  /  /  /  /  /  /  /  /        lawn
|                     /  /  /  /  /  /  /  /  /  /
|                   /  /  /  /  /  /  /  /  /  /
|                 /  /  /  /  /  /  /  /  /  /
|               /  /  /  /  /  /  /  /  /  /
|             /  /  /  /  /  /  /  /  /  /
|           /  /  /  /  /  /  /  /  /  /
|         /  /  /  /  /  /  /  /  /  /
|       /  /  /  /  /  /  /  /  /  /
|     /  /  /  /  /  /  /  /  /  /
|   /  /  /  /  /  /  /  /  /  /
| /  /  /  /  /  /  /  /  /  /
O----------------------------------------------------------> time
 <-><-><-><-><-><-><-><-><-><------- t minutes ------>
 9 intervals of t/8 minutes

Let the time each snail is on the lawn be t minutes, the velocity of
a snail v centimeters per minute, and the width of the lawn v*t
centimeters. 

After the first snail traverses 1/8 of the lawn, or v*t/8 meters, the 
second snail can begin. This takes the first snail (v*t/8)/v = t/8 
minutes. 

After eight more of these time intervals, the tenth and last snail 
begins his journey, at time 9*t/8. It takes him t minutes to cross the 
lawn, so we get the equation 9*t/8 + t = 50.  

We solve this equation for t, noting that the solution is independent 
of the value of v.

-Doctor Rob,  The Math Forum
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