Saving fuel the maths way.

Assumption 1: Petrol usage is proportional to driving time and driving speed

The longer you drive, the more fuel you use. Duh?
The faster you drive, the more fuel you use. Duh too. Dunno how proportional though. [1]
Proportional when both are considered? Not so duh. Probably not but let's just assume they are.

Assumption 2: The proportionalities of time and speed are independent of each other.
Assumption 3: Total petrol usage is petrol usage from driving time + petrol usage from driving speed.

K those are some pretty bold assumptions but they make sense.

Total petrol (fuel) usage = Fu
Petrol usage from driving time = Fa
Petrol usage from driving speed = Fb

Fa α t, t = driving time
Fb α v, v = driving speed
Fa = kt
Fb = pv, k and p are constants.

Fu = Fa + Fb
Fu = kt + pv

Now we know distance, D = vt
so v = D/t

Fu = kt + pD/t
To find minimum fuel consumption, we differentiate

dFu/dt = d/dt (kt + pD/t) = k - pD/t²
At minimum, dFu/dt = 0, k - pD/t² = 0

k = pD/t²
t² = pD/k
t = √(pD/k) = √(pDk)/k
v = D/t = D/√(pD/k)
v = √(pkD)/p
So, to save as much fuel as you can, drive with speed √(pkD)/p. The journey will take √(pDk)/k. Constants p and k can be found through expensive experiments. If anyone finds them for Honda City, tell me.


[1]
Does fuel usage really increase with increasing speed? Consider this:
At a constant speed, resultant forces = 0
Friction = Work done by engine
Friction is limited at µR, R = reaction force on ground by car.
Thus, work done by engine is limited.
So, to maintain a speed, no matter how high or low, takes the same amount of fuel!
Accelerating to that speed is another matter.

Mathmaticious.

LOL