# Fuel Economy of Automobiles

## We gave both cars 10 litres of fuel. We put them in a race against each other and compared how farther the Rainbow model S Hybrid goes than the Rainbow Model Z.

we mechanically engineered both the cars to run at the same speed and never stop until the car stopped due to no Fuel. It was tested on a straight race track so their would be no or minimal bias occurring within the Data.

## Graph displaying the Performance Results of Both cars.

Blue: Rainbow Model Z

Red: Rainbow Model S Hybrid

Both the cars performed well in the race against each other. However overall, the Rainbow Model S Hybrid went 2 meters further than the Rainbow Model Z. There was one problem though, the Rainbow Model Z got a full kilometer head start than the S Hybrid. So we decided to perform some calculations to calculate how far both the cars would travel Distance/Litre.

Rainbow Model S Hybrid:

(10,23)

(8,18.6)

m = Delta y / Delta x

m = 18.6 - 23 / 8 - 10

m = -4.4 / 2

m = 2.2

y - intercept

Therefore we can substitute the values into y = mx + b as:

y = 2.2x + 1

Rainbow Model Z:

(10,25.7)

(8,20.56)

m = Delta y / Delta x

m = 20.56 - 25.7 / 8 - 10

m = -5.14 / -2

m= 2.57

y - intercept = none

Therefore we can substitute the values in the equation y = mx + b as:

y = 2.57x

## Our Results So Far Conclude

With the equations given, we can easily interpolate and extrapolate to find other values by substituting the value of either x or y if given.

We acknowledge that there was a 1 kilometer head start given to the non-hybrid, so we can take out the y - intercept for the car's equation to make a fair comparison.

The 2 lines intersect at (2.7, 6.946)

This means the following:

- Up until 2.7 litres of fuel the non - hybrid seems to be better as it is travelling further

- The hybrid seems less convenient up until the 2.7 litres mark

- The hybrid seems as it is a more fuel efficient car than the non - hybrid after the 2.7 litres mark.

## However the company realized

The company realized that there was an error in the data since a 1 kilometer head start does not mean anything when measuring fuel efficiency.

So they tested both cars again starting them both at point (0,0) and the results where simple and the same, just clearer to see how more efficient the hybrid was compared to the non - hybrid.

The equations for both the lines were the same as before, however since the Rainbow Model Z did not have a 1 kilometer head start this time, we removed the y - intercept of it's equation leaving us with

y = 2.2x

and the equation for the Rainbow Model S hybrid was still

y = 2.57x

Therefore the company concluded that the Rainbow Model S Hybrid was more efficient than the Rainbow Model Z as it traveled 2.7 km more than the non - hybrid car with both cars filled up with 10 litres of fuel.