# Fuel Economy is terrible, at 0.65L per km; develop linear model for remaining fuel

#### lavagirl

##### New member
Adams Car has terribble fuel economy, approximately 0.65L per km. Develop a linear model of adams car that represents the fuel remaining in the tank, A, s a function of the distance, dkm, the car could travel from that date, assuming the tank has 85L of fuel remaining on day 1.

A= remaining fuel
d = kilometres
m= L/Km
N fuel tank capacity

#### Subhotosh Khan

##### Super Moderator
Staff member
Adams Car has terribble fuel economy, approximately 0.65L per km. Develop a linear model of adams car that represents the fuel remaining in the tank, A, s a function of the distance, dkm, the car could travel from that date, assuming the tank has 85L of fuel remaining on day 1.

A= remaining fuel
d = kilometres
m= L/Km
N fuel tank capacity
What are your thoughts?

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#### HallsofIvy

##### Elite Member
You want "remaining fuel" to be a function of "distance driven", A= f(d). In fact, you are told to make it a linear function so A= pd+ q for some numbers p and q. You just need to find correct values for p and q. Suppose d= 0. That is, suppose you haven't driven any distance at all. How much fuel is left in your tank? If d= 0, A= p(0)+ q= q so that is q. Suppose you drive 100 km so d= 100. A= 100p+ q. How much fuel is used driving 100 km? So how much fuel do you have left? Set that equal to A in A= 100p+ q. Since you already have found q, you have a simple equation to solve for p.

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