Hybrid and electric cars have gained in popularity in the last decade as a consequence of high gas prices. But their great gas mileages often come with higher car prices. There may be savings, but how much and how long before those savings are realized?

Suppose you are considering buying a Toyota Prius, which starts around $25,000 and gets 50 mpg. A similarly equipped Honda Accord will run closer to $22,000 but will get 31 mpg. How long would it take for the Prius to recoup the price difference with its lower fuel costs, assuming you drive 1,000 miles per month?

First, use the following formula for gas savings, where GM stands for gas mileage, to determine how far you will need to drive to recoup the cost difference in the vehicles. Use the known values and the average price of gas in your area to write a specific equation. Determine the type of equation that results, and then solve it algebraically.

$save=$gasDistance1GMnow1GMimproved

Choose a different hybrid or electric car that gets high gas mileage and compare it in a similar way to a gas-powered car in which you are interested that gets lower gas mileage. How long will it take to recoup the price difference for the miles you drive permonth?

Because of these results, it is reasonable to be concerned that the benefits of a hybrid car might not outweigh the initial higher cost. How efficient would the hybrid need to be in order to recoup a $3,000 price difference within 10 years if the standard vehicle gets 25 mpg? Both the improved gas mileage and the distance driven per year play a role.

To analyze the situation, use Excel to determine the miles that need to be driven to save $3,000 at various gas mileages, from 26 mpg to as high as 100 mpg. Then convert each number of miles into a number of years by considering three possibilities for the number of miles driven per year.

he set-up below is one of several possible ways to begin answering this problem.

We can compare hybrid and gas-powered cars ...

(provide

a few details from the problem statement to summarize the

situation)

using the equation ...

(show

the

equation).

Assuming that gas costs ... (insert average price of gas in your

area),

the equation becomes ?

(state

the equation with the known

values).

This is a ...

(state

the type of

equation).

To solve it ?

(explain

how to solve it, and provide a

solution).

Assuming we drive 1,000 miles per month ...

(show

the calculation needed, and explain how long it will take to recoup the price

difference).

We can compare ...

(choose

two cars to compare and state their prices and gas

mileages).

Assuming that gas costs ... (insert average price of gas in your area), the equation becomes ...

(state

the equation with the known

values).

This is a ...

(state

the type of

equation).

To solve it ...

(explain

how to solve it, and provide a

solution).

Assuming we drive ...

(state

the number of miles you drive per month or per

year),

it will take ...

(show

the calculation needed, and explain how long it will take to recoup the price difference. Comment on the

results).

We can use Excel ...

(explain

how to set up the

spreadsheet)

and the following equation ...

(state

the equation with the known

values).

The columns in the spreadsheet ...

(explain

how each column in the spreadsheet is calculated, using the equation to get the distance needed to recoup the

cost).

From the spreadsheet ...

(include

the spreadsheet, and explain how the number of years to recoup the cost for each of the three assumed yearly mileages is

calculated).

The number of years needed ...

(state

the required better gas mileage for each of the three assumed yearly

mileages).