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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
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figure out the total time, and the total distance divide the total distance by the total time
ok it was easy but i got it wrong total distance is \(2\times 160=320\)
time going in your new red porche is \(\frac{160}{80}=2\)

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Other answers:

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

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