Question 353603: A young woman decides to drive to her Grandma's house, which is 120 miles away. Because she's not particularly eager to get there, she gets on the highway and sets the cruise control for 40 miles an hour.
She drives 120 miles to Grandma's house. Her new car has a little computer that tells her that her average speed is 40 miles an hour.
When she gets there, she talks to Grandma and high tails it out of there; she's eager to get home. She sets the cruise control for 60 miles an hour.
She travels the same road and the same 120 miles. When she gets home, she does a little figuring. She says, "I drove 120 miles up, 120 miles back, or 240 miles. I drove 40 miles an hour up, and 60 miles an hour back, so my average speed was 50 miles an hour, and it should have taken me 4.8 hours. But it took me 5 hours!"
I understand that its because:
trip A= distance 120/40 speed= 3 hours and
trip B= distance 120/60 speed= 2 hours therefore 3 hours + 2 hours = 5 hours and
Full trip= distance 240/50 total average speed= 4.8 hours
but how is that so? How is it that when you average it you get a different answer?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
That's because your assertion that the average speed is 50 mph is incorrect. The average speed is the total distance, 240 miles, divided by the total time, 5 hours, which is equal to 48 miles per hour.
Here's another illustration of the same thing. You have a convenience store that is some distance  from your house. When you drive to the store, there is some traffic, so you can only manage 25 miles per hour. On the return trip you make 35 miles per hour. What is your average speed?
It takes you  hours to make the outbound trip. It takes  hours to come home. Since you go 25 mph outbound we can say:
Likewise
So the total time is
The total distance traveled is  because you go out and back again, hence the average rate is then the total distance divided by the total time:
\ =\ 29.1\overline{6})
29 and 1/6 miles per hour, not 30 as most people would guess.
John
My calculator said it, I believe it, that settles it
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