lalala wrote:hi guys! can i have help with any of these questions on my homework assignment i just dont get it.

The best tool in your math toolbox is something called UNIT ANALYSIS. Using it you can solve for just about anything.

Lets do these one at a time:

lalala wrote:4. If one Deutschmark is worth 55 cents and gasoline costs 1.30 Deutschmarks per liter, what is the cost in dollars per gallon?

OK, so you know that:

One Deutschmark is worth 55 cents

Gasoline costs 1.30 Deutschmarks per liter.

You want to know the cost is in dollars per gallon

The first thing we do is put in our starting point: the price in Deutschmarks per liter (DM/l)

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`1.30 DM |`

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l |

Now, we'll use the fact that one DM is 55 cents (0.55 dollars) to get the price in dollars per liter. If we multiply 1.30 DM by 0.55 dollars per DM, DM cancels, and we get dollars.

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`1.30 DM | 0.55 $ |`

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l | 1 DM |

If you solve this now, you'll get 0.715 dollars/liter. But wait, there's more!

Let's convert liters to gallons as well. One gallon is 3.785 liters, so:

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`1.30 DM | 0.55 $ | 3.785 l |`

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l | 1 DM | 1 gal |

NOW, we'll cancel out the units and multiply through: DM's cancel out, and liters cancel out, which leaves us with:

1.30 times 0.55 dollars times 3.785 on the top and 1 times 1 times 1 gallon on the bottom.

Multiplying that through we get 2.7063 dollars divided by one gallon, or 2.7063 dollars per gallon.

lalala wrote:6. The concorde is the fastest airliner used for commercial; it can cruise at 1450 mph:

a. What is the cruise speed of the Concorde in mi/s?

b. What is the cruise speed of the concorde in m/s?

This one's actually easier - Its already broken down into steps.

1450 miles per hours, or 1450 mi/hr is that starting value.

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`1450 m |`

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hr |

We know that there are 60 minutes per hour, so lets put that in.

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`1450 m | 1 hr |`

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hr | 60 min |

Now lets convert minutes to second: 60 seconds is one minute:

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`1450 m | 1 hr | 1 min |`

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hr | 60 min | 60 sec |

Now we can cancel out and simplify to 1450 divided by 60 times 60.

1450 mi / 60*60 sec

1450 / 3600 sec

0.4027 mi/sec

for part b, we need to convert 0.4027 mi/sec to meters per second. there are 1609.34 meters in a mile, so by multiplying miles per second by meters per mile...

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`0.4027 mi | 1609.34 m |`

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sec | mi |

So, we cancel miles out, and multiply 0.4027 by 1609.34 to get 648.08 m/sec.

lalala wrote:7. The gasoline consumption of a small car is 15 km/L. How many miles per gallon is this?

8. The speed limit on a highway in Lower Slobbovia was given as 120,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1/8 mile, and a fortnight is 14 days.?)

I'm going to leave these last two for you to work out, if you can. For number seven, you need to convert kilometers to miles, and liters to gallons. You can get those covnersions at the main page of this web site. The last one is way too easy. They gave you all the numbers you need.

Best of luck! I look forward to seeing your answers!

William J. Knight

Health Physicist

Los Alamos National Labs