Question

Suppose that you drive 30000 miles per year and gas averages $4 per gallon.

Answer 1

Answer:

Let's set up some ratios/rates to find out the annual cost of driving an SUV.

Traveling 30,000 miles at 9 miles per gallon and $4 a gallon, how much do you spend?

30,000 miles 1 gallon $ 4

----------------- x ---------------- x -------------- = $ X per year

1 year 9 miles 1 gallon

We set it up this way so we can negate similar units in numerators and denominators.

(30,000 miles)(1 gallon)($4) $ X

------------------------------------- = ------

(1 year)(9 miles)(1 gallon) year

120,000 miles•gallon•$ $ X

------------------------------ = ------

9 year•miles•gallon year

For units, miles and gallons negate but not $ because there is no $ unit in the denominator and not years because no year in numerator, so you are left with

120,000 $

------------- = $13,333.33 per year driving the SUV.

9 year

Now let's find the cost per year driving a hybrid going the same distance using the same rate for gas cost but a different rate for gas usage. The hybrid uses 30 miles for every gallon.

30,000 miles 1 gallon $4

------------------ x ------------ x ------------ = $ X per year

1 year 30 miles 1 gallon

(30,000 miles)(1 gallon)($4)

------------------------------------ = $ X per year

(1 year)(30 miles)(1 gallon)

120,000 miles•gallon•$

------------------------------- = $ X per year

30 years•miles•gallon

120,000 $ $4,000

-------------- = --------- driving the hybrid

30 years year

The ultimate question is how much more will you save annually driving the hybrid over the SUV?

SUV $13,333.33 per year - hybrid $4,000 per year = $9,333.33 savings per year