Linear Model/algebra/functions Question

[joshua14699]

Mr Bean’s car has terrible fuel economy, approximately 0.65 litres per km. Develop a linear
model of Mr Bean’s car that represents the fuel remaining in the tank, A, as a function of the
distance (in km), d, the car could travel from that date, similar to the three completed in Task 1(e),
assuming the tank has 85 litres of fuel remaining on the same day as you estimated the amount of
fuel remaining in the other three cars.

So for task 1(e) I created linear models in the from of A=-md + N
where A is fuel remaining, m is fuel economy as L/km, d is distance in km and N is total fuel tank capacity.
So I don't want a solution, just asking for ideas or ways to solve it.

An idea:
85=-0.65d + N
for d, N = 0
for N, d = 0

 

[susu123]

how to solve the question?

I see your problem as simple as:
A car consumes 0.65 litres of fuel per km.
What distance does the car travels with A litres of fuel?

And the solution as simple as:
L = Litres per km
D = Distance travelled with A litres

D = A / L

How would the question be solved then, what would the linear model of Mr Bean's car be?

 

[Otis]

Develop a linear
model of Mr Bean’s car that represents the fuel remaining in the tank, A, as a function of the
distance (in km), d, the car could travel from that date

Hi there.

What date?

assuming the tank has 85 litres of fuel remaining on the same day as you estimated the amount of
fuel remaining in the other three cars.

Not sure what a day or other cars have to do with Mr. Bean's fuel. :???:

So for task 1(e) I created linear models in the from of A=-md + N
where A is fuel remaining, m is fuel economy as L/km, d is distance in km and N is total fuel tank capacity.


An idea:
85=-0.65d + N
for d, N = 0 This says that the tank holds no gas.
for N, d = 0 This means Mr. Bean's car hasn't gone anywhere, yet (a Nova maybe).

Is the tank capacity necessary?

It makes sense to let N = liters of fuel at mile 0. In other words, you start keeping track of the remaining fuel at the point where the tank has 85 liters remaining. You also reset the trip odometer, at this point.

A = -0.65d + 85

Now, if the car has not been driven since, then d = 0 and A = 85

For each kilometer of distance driven, this model reduces the 85 liters by 0.65 liters; hence, the resulting number is the amount of fuel remaining.

As part of your answer, you ought to state the domain for d. In other words, how big can d get, without the model reporting a negative amount of remaining fuel?

My interpretation of the requested model may be wrong, if dates, days, other cars, and tank capacities are somehow relevant.

Cheers :cool: