anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
figure out the total time, and the total distance divide the total distance by the total time
anonymous
  • anonymous
ok it was easy but i got it wrong total distance is \(2\times 160=320\)
anonymous
  • anonymous
time going in your new red porche is \(\frac{160}{80}=2\)

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anonymous
  • anonymous
how about the time returning?
anonymous
  • anonymous
ugh i don't know cause it comes out as a decimal?
anonymous
  • anonymous
much easier (believe it or not) if you leave it as a fraction
anonymous
  • anonymous
in other words, take \(\frac{160}{48}\) and instead of writing it as a repeating decimal, reduce it to \(\frac{10}{3}\)
anonymous
  • anonymous
so far so good?
anonymous
  • anonymous
okay so? then do i leave the other as 2? or 160/2?
anonymous
  • anonymous
no use 2
anonymous
  • anonymous
now the next job is to total up the time, in other words compute \[2+\frac{10}{3}\] leave it as a fraction
anonymous
  • anonymous
okay then what?
anonymous
  • anonymous
16/3
anonymous
  • anonymous
right and now speed is distance divided by rate
anonymous
  • anonymous
so your final job is \[320\div \frac{16}{3}\]
anonymous
  • anonymous
So the average is 60?
anonymous
  • anonymous
that is what i get too
anonymous
  • anonymous
kay good. Thank you!!
anonymous
  • anonymous
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
  • anonymous
you could drive 160 miles or 100 miles or 3,000 miles or \(m\) miles, the average will still be 60
anonymous
  • anonymous
Okay Thank you soo much. =)
anonymous
  • anonymous
yw
anonymous
  • anonymous
try it with \(m\) you get \[\frac{2m}{\frac{m}{80}+\frac{m}{48}}=60\] after some algebra

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