A Crabby Word Problem
Date: 2/13/96 at 17:34:28 From: Anonymous Subject: A crab trying to swim home... Dr. Math, Our class had the following problem the other day: A crab was trying to swim home after lying on the beach. Its home was 35 meters out in the ocean. It took the crab one minute to swim ten meters. Then a wave would wash it back five meters, where it would rest for one minute before trying again. If the crab continued this way, how long did it take the crab to get home? I can see where 11, 13, 16 and 18 minutes could be possible solutions to the problem. What might I be doing wrong?
Date: 2/13/96 at 19:0:41 From: Doctor Ethan Subject: Re: A crab trying to swim home... Thanks for the very interesting problem! Let's consider the crab after it has advanced 5 times, been washed back 5 times, and rested 5 times. At this point, the crab is 25 meters out and about to start advancing again. At its farthest up until this point, the crab has reached the 30 meter mark. (It has just been washed back and rested.) This procedure has taken 10 minutes. (From the problem description I am assuming that only the advancing and rest periods take any time - it seems that the wash back is instantaneous.) So now we are at the 10-minute mark, and the crab begins advancing again. After a minute it has gone from 25 to 35 meters out, thus reaching its home after 11 meters. Admittedly, it may be washed back in moments, but it has, in fact, reached its home. Perhaps the crab has built its home well, and will be able to find shelter there from those pesky waves. -Doctor Ethan, The Math Forum
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