Grades 9-10 Video Solutions 2021-video 2021 9-10/11

Video Transcription

Problem number 11 states, Tom had 10 sparklers of the same size. He lit one first. When only a tenth of it remained, he lit the second one.  When only a tenth of that remained, he lit the third one, and so on. The sparklers burn at the same rate along their entire length. One sparkler will burn in two minutes.  How long does it take for all 10 sparklers to burn down? So here we have our 10 sparklers. On the left, we have the number of minutes that have passed in this simulation that we  are about to run. So the first sparkler burns nine-tenths of its original size, and it takes two minutes  to burn the entire sparkler, so in order to burn nine-tenths of the two minutes, we would do two minutes times nine-tenths, and we would get 1.8 minutes.  By multiplying the 0.8 by 60 minutes, that would get us 48 seconds, but we'll leave it in terms of decimals so the addition is a little bit simpler.  So this means that at this point, we are 1.8 minutes into our simulation, and at this point, the second sparkler is lit.  One point eight minutes later, we know that the second sparkler will have burned nine-tenths of the way through.  That means at this point, we are 1.8 times two minutes into the simulation, and the third sparkler gets lit.  By the time the fourth sparkler gets lit, another 1.8 minutes has passed, so now we are at 1.8 times three minutes.  Let's continue the trend, and by the time the tenth sparkler is down at its nine-tenth point, the time elapsed would be 1.8 times 10.  Now we just need to add the time that it takes for the sparkler to completely burn out. So it would be one-tenth times two minutes for it to burn out completely.  That would be 0.2 minutes. So in total, when the last sparkler burns out, we get 1.8 times 10 plus 0.2 minutes. So 18 plus 0.2, which is 18.2.  By multiplying the 0.2 by 60, we can get that it is 18 minutes and 12 seconds. So that is our final time.  So the question asked us, how long did it take for all ten sparklers to burn down? The answer is 18 minutes and 12 seconds. Letter B.

Video Summary

Tom had 10 identical sparklers, each burning completely in two minutes. He lights each subsequent sparkler when only one-tenth of the previous one remains. This means each sparkler burns nine-tenths of its length before the next is lit. Each nine-tenths burn lasts 1.8 minutes (calculated as 9/10 of 2 minutes). After lighting all 10 sparklers successively, the remaining one-tenth of the last sparkler burns in 0.2 minutes. Therefore, the total burn time is 18.2 minutes, which translates to 18 minutes and 12 seconds. The total time for all sparklers to burn is 18 minutes and 12 seconds.

Keywords

sparklers

burn time

lighting sequence

total duration

calculation