Snails Crossing the LawnDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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