Question

part 4: the road trip
you are planning a road trip from toronto to montreal, a distance of about 550 km. your cars fuel efficiency is 8 l/100 km, meaning it uses 8 litres of gasoline for every 100 kilometres driven. the average price of gas is $1.65 per litre.

1. calculate the total amount of gasoline (in litres) needed for the entire 550 km trip.

(hint: you can set up a proportion or use the rate)
total litres needed: ____ l

1. calculate the total cost of gasoline for the trip

total fuel cost: $ ____

1. bonus: your friend says that if you drive faster, your fuel efficiency gets worse. assume that driving 10% faster makes the car use 15% more fuel. calculate the new fuel cost if you drive 10% faster.

(hint: start by determining the new, less efficient fuel rate)
new total fuel cost: $ ____

Explanation:

Step1: Calculate fuel needed

Set up a proportion. Let $x$ be the litres of fuel needed. $\frac{8}{100}=\frac{x}{550}$, then $x=\frac{8\times550}{100}$.
$x = 44$ L

Step2: Calculate total fuel cost

Multiply the total litres by the price per litre. The price per litre is $\$1.65$. So the total cost $C = 44\times1.65$.
$C=\$72.6$

Step3: Calculate new fuel - rate

The original fuel - rate is $8$ L/100 km. If driving 10% faster makes the car use 15% more fuel, the new fuel - rate $r$ is $r=8\times(1 + 0.15)$.
$r = 8\times1.15=9.2$ L/100 km

Step4: Calculate new total litres needed

Using the new fuel - rate and the distance of 550 km. Let $y$ be the new litres needed. $\frac{y}{550}=\frac{9.2}{100}$, then $y=\frac{9.2\times550}{100}$.
$y = 50.6$ L

Step5: Calculate new total fuel cost

Multiply the new total litres by the price per litre. The new total cost $C_{new}=50.6\times1.65$.
$C_{new}=\$83.49$

Answer:

Total Litres Needed: 44 L
Total Fuel Cost: $\$72.6$
New Total Fuel Cost: $\$83.49$