# Conversions travel problem

#### bigman8424

how long, in months to 3 sig. figs, would it take someone traveling 27500 mi/hr to go 1.43*10^12 meters

plz help, i'm horrible at conversions

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#### dextercioby

Homework Helper
What's the connection between time,speed and distance...?

Daniel.

#### saltydog

Homework Helper
Tell you what big dude, figure that one then figure how far light travels in one nanosecond. I'm guessing about 10 feet. You finish yours, then try and work on mine. I'll let a day go by and then post how I figured it out if you still haven't done so.

#### saltydog

Homework Helper
saltydog said:
Tell you what big dude, figure that one then figure how far light travels in one nanosecond. I'm guessing about 10 feet. You finish yours, then try and work on mine. I'll let a day go by and then post how I figured it out if you still haven't done so.
Oh yea, I didnt' forget: How far does light go in a nanometer:

The important thing to remember about conversions is to arrange the quotients so that the units cancel. That's the purpose of this exercise:

So we have:

$$\text{Speed of light: }\frac{186000\quad\text{miles}}{1\quad\text{second}}$$

$$\text{feet in a mile:}\frac{5280\quad\text{feet}}{1\quad\text{mile}}$$

$$\text{nanoseconds in a second:}\frac{10^9\quad\text{nanoseconds}}{1\quad\text{second}}$$

So:

$$\frac{186000\quad\text{miles}}{1\quad\text{second}}*\frac{5280\quad\text{feet}}{1\quad\text{mile}}*\frac{1\quad\text{second}}{10^9\quad\text{nanoseconds}}$$

Note how the units cancel leaving feet/nanosecond. It's about 1 foot. It's the same way with all the other conversion problems: Arrange the quotients so that the units cancel leaving you with what you want.

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