March 2010
Problem of the Month

Prius Problem #2

In our first trip from Fort Collins to Estes Park in our Pius, we averaged 47.8 mpg on the way up, but 92.2 mpg on the way home (there is an elevation difference of more than 3,000 feet between Fort Collins and Estes Park).

What was our average miles per gallon over the whole trip if the distances up and back were the same?

Solution to the Problem:

The average mpg over the whole trip is 62.95 or 63 mpg.

You cannot simply add the two averages together and divide by two.

To find mpg, you must divide total miles by the total gallons.

Let y = miles from Fort Collins to Estes Park (you can actually use any value here).

Let x = the MPG over the entire trip.
Set up the following table to help you solve it:

	MPG	Gallons	Miles
Up	47.8	y / 47.8	y
Down	92.2	y / 92.2	y
Roundtrip	x	2y / x	2y

The number of gallons used on the way up plus the number of gallons used on the way down must equal the total number of gallons, so this gives us our equation:

y / 47.8 + y / 92.2 = 2y / x

Dividing by y, we obtain:
1 / 47.8 + 1 / 92.2 = 2 / x

Then .0317 = 2 / x,
so x = 62.95 or 63 mpg.

Correctly solved by:

1. David & Judy Dixon

Bennettsville, South Carolina

Send any comments or questions to: David Pleacher