## EXOEXOEXO one year ago it took matt twice the time to drive from home to work as it took him to drive back home from work by the same route. if matt averaged 30 miles per hour(mph) on his drive to work, his average speed for the entire round trip was?

1. anonymous

ok so if it was 2 times as fast what would his drive backs mph be?

2. EXOEXOEXO

60?

3. anonymous

yea

4. anonymous

so since you have both of them how do you find the average

5. EXOEXOEXO

(30+60)/2?

6. anonymous

yea so 45 would be it :)

7. EXOEXOEXO

but its not an answer choice

8. anonymous

what are the choices???

9. anonymous

lol its not twice as fast its twice as slow

10. EXOEXOEXO

30 25 40 15

11. anonymous

so (15+30)/2

12. anonymous

wait a minute

13. anonymous

@dan815 am i right in saying (15+30)/2 sorry im tired

14. anonymous

lol wait i think im just being dumb

15. anonymous

no wait im not it would be 22.5 mph are you sure thats the whole question

16. EXOEXOEXO

I think it is a 30+2(15)/2

17. anonymous

no then that would just be 30

18. EXOEXOEXO

30 mph is the average on Matt's drive to work while 15 mph is the average of Matt's drive to home from work

19. anonymous

because he took twice as long using the same rounte meaning he was twice as slow (15 mph) and the other was 30 so the avarage of that is 22.5mph

20. anonymous

yea

21. anonymous

so basicly in the context of the problem x= matts time from work so (x+(x/2))/2= avg

22. anonymous

and x=30 so

23. anonymous

yea

24. anonymous

cool @EXOEXOEXO ???

25. anonymous

although its not a choice it is the right answer for what you gave me

26. EXOEXOEXO

lol

27. anonymous

haha yea unless you made a typing error??

28. EXOEXOEXO

I don't think I made one

29. whpalmer4

How long does it take him to drive to work? How long does it take him to drive home? Add them together to get the round trip time. Average speed for the round trip is round trip distance divided by round trip time.

30. anonymous

yea but thats not a choice :(

31. whpalmer4

That's all the information you need to calculate the answer... Let the distance to work be $$x$$. Time to drive to work is $$x/30$$. Time to drive home is $$(1/2)*(x/30)$$ Total distance driven is $$2x$$ Average speed for trip is total distance driven divided by total time.

32. anonymous

yea i know that and you would get 22.5 but thats not an answer choice for him

33. whpalmer4

No, 22.5 is not the result of that calculation, correctly done.

34. whpalmer4

Time to drive to work is $\frac{x}{30}$ Time to drive home is$\frac{1}{2}*\frac{x}{30} = \frac{x}{60}$ Total time driving is $\frac{x}{30}+\frac{x}{60} = \frac{3x}{60} = \frac{x}{20}$ average speed is $\frac{2x}{\frac{x}{20}}=2x*\frac{20}{x} =$

35. whpalmer4

Or, pick a distance, any distance, and work out the problem. Let's say it is 60 miles to work, to make the arithmetic easy. 60 miles at 30 miles per hour = 2 hours to drive to work Driving home takes 1/2 the time, so that's 1 hour to drive home. Total distance driven is 60+60 = 120 miles. Total time driving is 2+1 hours = 3 hours Average speed =