Duration of a Clock's StrikeDate: 01/21/2004 at 19:50:30 From: Stacey Subject: how long does it take for a clock to strike 10 If it takes seven seconds for a clock to strike 7 o'clock, then how long does it take to strike 10 o'clock? It seems as if the answer is 10, but I have worked a problem just like this before and I can't remember how to start it. Date: 01/22/2004 at 09:04:23 From: Doctor Peterson Subject: Re: how long does it take for a clock to strike 10 Hi, Stacey. The answer depends on how you think of a strike. If each "bong" lasts until the next one starts, and you are counting how long the sounds last, then you are right: strikes 1 2 3 4 5 6 7 *=====*=====*=====*=====*=====*=====*===== +-----+-----+-----+-----+-----+-----+-----+ seconds 0 1 2 3 4 5 6 7 Each strike takes a whole second, and ten of them will take 10 seconds. But if you think only of the actual strikes (when the bell is hit), and ignore how long the sound lasts afterward, then the picture is different: strikes 1 2 3 4 5 6 7 * * * * * * * +-----+-----+-----+-----+-----+-----+-----+ seconds 0 1 2 3 4 5 6 7 Now there are 6 spaces BETWEEN strikes, which each last MORE than a second. Can you finish the problem, interpreting it that way? Of course, in reality each bong would take some time that may be more or less than the time between strikes, and we don't have enough information to determine the total time we hear the clock. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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