Question

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?

Answer 1

figure out the total time, and the total distance
divide the total distance by the total time

Answer 2

ok it was easy but i got it wrong
total distance is \(2\times 160=320\)

Answer 3

time going in your new red porche is \(\frac{160}{80}=2\)

Answer 4

how about the time returning?

Answer 5

ugh i don't know cause it comes out as a decimal?

Answer 6

much easier (believe it or not) if you leave it as a fraction

Answer 7

in other words, take \(\frac{160}{48}\) and instead of writing it as a repeating decimal, reduce it to \(\frac{10}{3}\)

Answer 8

so far so good?

Answer 9

okay so? then do i leave the other as 2? or 160/2?

Answer 10

no use 2

Answer 11

now the next job is to total up the time, in other words compute
\[2+\frac{10}{3}\]
leave it as a fraction

Answer 12

okay then what?

Answer 13

16/3

Answer 14

right
and now speed is distance divided by rate

Answer 15

so your final job is
\[320\div \frac{16}{3}\]

Answer 16

So the average is 60?

Answer 17

that is what i get too

Answer 18

kay good. Thank you!!

Answer 19

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

Answer 20

you could drive 160 miles or 100 miles or 3,000 miles or \(m\) miles, the average will still be 60

Answer 21

Okay Thank you soo much. =)

Answer 22

yw

Answer 23

try it with \(m\)
you get
\[\frac{2m}{\frac{m}{80}+\frac{m}{48}}=60\] after some algebra