# Question #a0596

Jun 4, 2014

The answer to two decimal places is $31.84 \text{ liters}$.

Here's how to solve the problem:

This is a unit conversion question. You're given that the car has a highway mileage of 41 mpg (AKA, miles per gallon).

We have to convert miles per gallon into kilometers per liter.

Distance: miles --> kilometers
Volume: gallons --> liters

I like to use scientific conversion, so I can change all of my units at once. Notice below that I set up my expression so that the original units cancel (miles and gallons disappear), and I am left with the desired units of kilometers per liter.

Using these conversions as given, I will plug them into my scientific conversion expression:

$1 \text{ mile" = 1.60934" kilometers}$
$1 \text{ gallon" = 3.78541" liters}$

$\left(41 \text{ miles")/(1" gallon") * (1.60934" kilometers")/(1" mile") * (1" gallon")/(3.78541" liters}\right)$

Multiplying and dividing out just the numbers, we are left with approximately 17.43. What are the units here?

Well, again, notice that the miles cancel out, and the gallons cancel out. In our numerator, we're left with units of kilometers over liters, or kilometers per liter (which is what we wanted, YaY!)

So $41 \text{ miles per gallon" = 17.43" kilometers per liter}$.

The last thing we have to do is calculate how many liters of gasoline we need in order to travel $555 \text{ kilometers}$. Using the number we just found, we find:

$555 \text{ kilometers" * (1" liter")/(17.43" kilometers") = 31.84" liters}$

In order to go $555 \text{ kilometers}$, the car will need $31.84 \text{ liters}$ of gasoline.