Question

Part A:

You select a rental package that includes a car with an average consumption of 6.00 \rm liters of fuel per 100 \rm km. Considering that in Europe the average fuel cost is 1.063 \rm euros/ liter, how much (in US dollars) will you spend in fuel on your trip? ___> 5,000km

Part B:

how many gallons of fuel would the rental care consume per mile?

Answer 1

\[1 EUR= 1.20 USD\]

Answer 2

Does it tell you how far your trip is?

Answer 3

5000km

Answer 4

Alright! Looks like you have a lot of unit stuff to do for this class, huh?

So you're looking at
6.00 L/km for your fuel efficiency,
1.063 Euro/L,
and ...

Answer 5

over 20 questions.... yeah

Answer 6

we have \[1 EUR= 1.20 USD\]

Answer 7

Haha, that's a lot! You'll get through them.

So about the \(1 EUR= 1.20 USD\). You know how when you have \(x=x\), then you can say, just as truly, that \(\large \frac{x}{x}=1\)?

Answer 8

right

Answer 9

When you do unit conversions, you want to do that with equal values.

Answer 10

That is,

Answer 11

\[\frac{1EUR}{1.20USD}=1=\frac{1.20USD}{1EUR}\]
The incredibly useful part is that if it's \(1\), you can multiply it by any amount without changing it!

You want this often. Like, I have 5 Euros.
\[5EUR=5EUR\times 1\\=5EUR \times \frac{1.20USD}{1EUR}\\=5\times\frac{1.20}{1}\times \frac{EUR\times USD}{EUR}\\=5.20\times \frac{\cancel{EUR}\times USD}{\cancel{EUR}}\]

Answer 12

Pfft, I messed up the \(5\times 1.20\)!

Answer 13

i am not sure if that is correct.... :/

Answer 14

It's 6.
5 Euro is $6USD.

Answer 15

but...... you forgot 6.00 \rm liters of fuel per 100 \rm km.

Answer 16

I was demonstrating a principle, sorry! It was just, arranging that 1Euro = 1.20 USD equation to be useful!

Answer 17

hmmm okay.

Answer 18

" `Alright! Looks like you have a lot of unit stuff to do for this class, huh?`
`So you're looking at`
`6.00 L/km for your fuel efficiency,`
`1.063 Euro/L,`
`and ... ` "
add 1.20 USD/Euro to that list.

Answer 19

Units can cancel, substitute, and multiply like variables, even though they're not variables.

Answer 20

So if you have 6 L/km, and 1.063 Euro/L, you can multiply to get Euro/km.

Just look at that until you really get it. It's that simple.

Answer 21

umm...

Answer 22

Haha, that means something is wrong or unclear! What's up? Oh, I see...

Answer 23

6 L/ 100km, and 1.063 Euro/L, you can multiply to get Euro/km.

Answer 24

That is\[(6\times 1.063 / 100)\times \frac{L\times EUR}{km\times L}\]

Answer 25

how would that give me USD ?

Answer 26

You now have EUR/km. Now is when you use that part I accidentally confused you with earlier, where you can multiply that by 1, where we used\[1 EUR= 1.20 USD\]toget\[1=1.20USD/1EUR\]

Answer 27

\[\frac{ 6L }{100km } \times \frac{ 1.063 Euro }{ 1L} \times \frac{ 1.20 USD }{ 1 Euro }\]

Answer 28

You mess with the units so they cancel out.

Exactly, so you were ahead of me, congrats! That gets you the units USD/km, and some value. Go one step further. You know how many kilometers the car traveled.
Multiply your "per km" amount by how many km's you went! I hope that makes sense.

Answer 29

\[6L/100km×1.063Euro/1L×1.20USD/1Euro \times 5000km?\]

Answer 30

Exactly!

I have to go, so good luck!

Looking at part B, use your L/km units, and find a km to mi conversion.

If it's an equation, make it equal 1 and use it - just like USD to Euros.

Also, I see Shane_B is on. Shane_B is smart and can help you in physics if you need!

Answer 31

Good luck on your problems!

Answer 32

shoot :( alright.....

Answer 33

@Shane_B could you help? I found part A, not part B...

Answer 34

eh, shoot im screwed. yay

Answer 35

Since I don't have long I'll skip all the reading and just post how I'd do both parts of the problem. For the first part it's telling you that your fuel consumption is:\[ \frac {6L}{100km}\]which simplifies to:\[\frac{0.06L}{1km}\]
If your trip is 5000km, just multiply it out to get your total consumption for the trip:
\[5000 \cancel{km} * \frac{0.06L}{1\cancel{km}}=300L\]So that's how much fuel the trip will take. Multiply that by the cost per L to get to total cost in Euros:
\[300\cancel{L}*\frac{1.083EU}{1\cancel{L}}=318.9EU\]Convert that to USD:\[318.9\cancel{EU}*\frac{1.20USD}{1\cancel{EU}}=382.68USD\]
Part B is just asking you to convert 300L to gallons. The conversion factor is:\[1gal=3.7853L\]So you end up with:\[300\cancel{L}*\frac{1gal}{3.7853\cancel{L}}=79.25gal\]
Hope this helps!

Answer 36

I guess I misread part B since it's asking for the total cost per mile and not the total gallons used. At any rate, the conversions work the same. I can work it out if you like

Answer 37

i figured it out, thank you!!! I appreciate it

Answer 38

good :)