Counting SecondsDate: 12/13/2002 at 18:29:29 From: James Yoder Subject: Word problem about time (seconds) Ali counted to 10, speaking a number every 5 seconds. How long did the complete count take? I thought the answer was 50, but my teacher says it's 45, because you start by saying "One" and going from there. So, if that were the case, wouldn't the answer be 46? Help! Date: 12/13/2002 at 23:39:05 From: Doctor Peterson Subject: Re: Word problem about time (seconds) Hi, James. The trouble here is that we don't know how long it takes to SAY one number, from opening the mouth to closing it. So your teacher is assuming that it takes no time at all, which is pretty close to reality (try saying "ten" and timing it!): "1 2 3 4 5 6 7 8 9 10" +----+----+----+----+----+----+----+----+----+ \___/\___/\___/\___/\___/\___/\___/\___/\___/ 5 5 5 5 5 5 5 5 5 = 9*5 = 45 sec Your answer of 50 assumes that Ali not only speaks one number every 5 seconds, but that it takes the full five seconds to say it: " 1 2 3 4 5 6 7 8 9 10 " ==== ==== ==== ==== ==== ==== ==== ==== ==== ==== +----+----+----+----+----+----+----+----+----+----+ \___/\___/\___/\___/\___/\___/\___/\___/\___/\___/ 5 5 5 5 5 5 5 5 5 5 = 10*5 = 50 sec Your new proposal seems to be that it takes one second to say each number: " 1 2 3 4 5 6 7 8 9 10 " = = = = = = = = = = +----+----+----+----+----+----+----+----+----++ \___/\___/\___/\___/\___/\___/\___/\___/\___/| 5 5 5 5 5 5 5 5 5 1 = 9*5+1 = 46 sec But there's really no reason to assume that. The best thing we can do is to say it will take 45 seconds PLUS however long it takes to say "ten". If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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