## jdlandreth Group Title 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? one year ago one year ago

1. satellite73 Group Title

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

2. satellite73 Group Title

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

3. satellite73 Group Title

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

4. satellite73 Group Title

5. jdlandreth Group Title

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

6. satellite73 Group Title

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

7. satellite73 Group Title

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

8. satellite73 Group Title

so far so good?

9. jdlandreth Group Title

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

10. satellite73 Group Title

no use 2

11. satellite73 Group Title

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

12. jdlandreth Group Title

okay then what?

13. jdlandreth Group Title

16/3

14. satellite73 Group Title

right and now speed is distance divided by rate

15. satellite73 Group Title

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

16. jdlandreth Group Title

So the average is 60?

17. satellite73 Group Title

that is what i get too

18. jdlandreth Group Title

kay good. Thank you!!

19. satellite73 Group Title

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

20. satellite73 Group Title

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

21. jdlandreth Group Title

Okay Thank you soo much. =)

22. satellite73 Group Title

yw

23. satellite73 Group Title

try it with $$m$$ you get $\frac{2m}{\frac{m}{80}+\frac{m}{48}}=60$ after some algebra