jdlandreth
you, in your new red Porsche, decide to make a 160km trip to Carolina Beach, traveling at 80km?hr. Your make a return trip at a rate of 48km?hr. What was your average speed for the entire trip?
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anonymous
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figure out the total time, and the total distance
divide the total distance by the total time
anonymous
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ok it was easy but i got it wrong
total distance is \(2\times 160=320\)
anonymous
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time going in your new red porche is \(\frac{160}{80}=2\)
anonymous
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how about the time returning?
jdlandreth
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ugh i don't know cause it comes out as a decimal?
anonymous
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much easier (believe it or not) if you leave it as a fraction
anonymous
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in other words, take \(\frac{160}{48}\) and instead of writing it as a repeating decimal, reduce it to \(\frac{10}{3}\)
anonymous
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so far so good?
jdlandreth
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okay so? then do i leave the other as 2? or 160/2?
anonymous
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no use 2
anonymous
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now the next job is to total up the time, in other words compute
\[2+\frac{10}{3}\]
leave it as a fraction
jdlandreth
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okay then what?
jdlandreth
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16/3
anonymous
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right
and now speed is distance divided by rate
anonymous
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so your final job is
\[320\div \frac{16}{3}\]
jdlandreth
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So the average is 60?
anonymous
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that is what i get too
jdlandreth
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kay good. Thank you!!
anonymous
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notice two things
1) the average speed is not the "average of the speeds" and
2) the 160 is a red herring
if you really want to impress your math teacher, show that it works no matter how far you drive
anonymous
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you could drive 160 miles or 100 miles or 3,000 miles or \(m\) miles, the average will still be 60
jdlandreth
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Okay Thank you soo much. =)
anonymous
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yw
anonymous
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try it with \(m\)
you get
\[\frac{2m}{\frac{m}{80}+\frac{m}{48}}=60\] after some algebra