Expert: Sherman D. - 5/23/2005

Question
This isn't a homework question, just a personal pickle. I take somebody different places and I'd like to calculate how much it costs me to get them there using the following variables, Gas Milage, Distance Traveled, and Price of Gas.

The equation I came up with is:
(Gas Milage) / (Distance Traveled) * (Price of Gas)

But what I found out is that when the Distance Traveled is greated than the Gas Milage, the result is a number less than 1, so the answer is faulty, I believe that in all other cases the answer is correct.

The first time I tried it, I had:
(19.9 MPG) / (16.5 mi.) * ($2.39) = $2.88

The next time I tried it, I had:
(17.4 MPG) / (23.5 mi.) * ($2.44) = $1.68

Based on known data, the price for the second ride should cost MORE, seeing as how it's worse gas milage, a further distance, and more expensive gas. Please develop an equation that will fit my needs.

Thank You,
Eric Pheterson
epheterson@gmail.com

Answer
GM is the amount of distance you can travle and only burn one gallon of gas.

The formula as you may already know is

GM = mpg
which in formula form, would look like this
GM = (miles)/(gallon)
so

Since you need to know how many gallons of gas you would have to get to get the amount you need and how much it would cost you to get that many gallons. The formula would be

g = (miles)/(GM)

to find how much it would cost, the formula would be

((miles)/(GM)) * cost = Full Cost

1st
19.9 = 16.5/g
g = 16.5/19.9
g = .829145728

now if it costs $2.99 per gallon, you get

2.99(.829145728) = $2.48

-----------------------------------------------------------

2nd
g = (23.5)/(17.4)
g = 1.350574713

2.44(1.350574713) = $3.30

So there was your problem, you had your formula done wrong.

I hope you understood my work and i hope i was helpful.

if you were to use the formula you used
(m/g)/m * cost = FV
((m/g)/(m/1)) * cost = FV
((m/g)*(1/m)) * cost = FV
(m/(gm)) * cost = FV
the m's cancel out
(1/g) * cost = FV

as you know, you are paying per gallon(cost * g), but the formula you use has (1/g) * cost instead of g * cost.