## jdlandreth 2 years ago 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?

1. satellite73

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

2. satellite73

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

3. satellite73

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

4. satellite73

5. jdlandreth

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

6. satellite73

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

7. satellite73

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

8. satellite73

so far so good?

9. jdlandreth

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

10. satellite73

no use 2

11. satellite73

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

okay then what?

13. jdlandreth

16/3

14. satellite73

right and now speed is distance divided by rate

15. satellite73

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

16. jdlandreth

So the average is 60?

17. satellite73

that is what i get too

18. jdlandreth

kay good. Thank you!!

19. satellite73

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

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

21. jdlandreth

Okay Thank you soo much. =)

22. satellite73

yw

23. satellite73

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