nigg777 wrote:

Could someone smart please explain to me why it's not just the average of all 3 if all 3 paths are equal? Why isn't it just 130/3?

I see that the formula makes sense and the result seems correct. It's messing with my brain.

If it would just be 1 way, where one third of the way he goes 30, one 40, and one 60, it would be 130/3.

nigg777 Lets dissect the fundamental formula first:

Total Distance (d) = Average Speed (s) x Total Time (t) ===>This means it takes a certain time=t to travel a certain distance=d at a speed=s.Don't continue reading until you get an image of what the equation and its explanation in bold states.

To reaffirm your understanding, ask yourself this question. If it took you

1 hour to go to your school and then

1 hour to come back home, what is the total time you travelled? Your answer should be 2 hours. (Explanation: Total time =

Time going to school +

time coming back home =

1 hour +

1 hour = 2 hours

You can also apply the same concept above to your understanding with regards to distance. Total distance = Distance going to school + Distance coming back home.

Now try to apply this concept to speeds. You just can't because it just doesn't make sense. (If you drove at 40 mph to school then came back home at 70 mph, does this mean you drove a total of 110mph? The concept of total speeds does not exist so far)

If you're good so far, the table below would fully answer your question.

_____________|

Distance |

Average Speed|

Time[/u]

Home to School|___ d ___|____ 30 _____| d/30School to Home|___ d ___|____ 40 _____| d/40Home to School|___ d ___|____ 60 _____| d/60Total_________|d+d+d=3d|_____ S ____ | d/30+d/40+d/60 (We added total distance travelled and we added total time taken to travel the total distance)

Now the average speed taken to travel the

total distance 3d in a total time of

d/30+d/40+d/60 is were you could apply the formula to get the

average speed S.

I hope that all makes sense, props to the gmatclub math book.