Expert: Chanda Walker - 4/21/2009

Question
Zach arrives from Phoenix to somewhere at 60mph. Zach drives back from
somewhere to Phoenix at 40mph. What is his average speed?
Is this just simply adding 60+40 and dividing by 2 to get 50mph?

Answer
No not quite . . .

Let x = the distance traveled between Phoenix and somewhere.

He took x/60 hours to get there.  (If the distance were 120miles you can see it would be 2 hours.)

Now, on the way back he took x/40 hours.

Let's sum these and you'll have how long he traveled.

x/60 + x/40 = 100x/2400 = x/24 hours.

So he traveled 2x miles in x/24 hours.

To get miles per hour you divide the number of miles you traveled (2x) and the number of hours it took you to travel them:

2x/(x/24) = 48 mph

A little counter-intuitive huh.  He traveled a longer length of time at the slower speed so the average is less than 50mph.

Let me know if I can help further.