Voyager 1 is currently moving at just over 38,100 mph and was launched 34 years ago:

1) How many hectometers away from the Earth is Voyager 1?  (remember 1 in = 2.54 cm), to make things a bit more practical, assume that the launch date was 34 years ago TODAY (don't worry about hours/min/sec) and that Voyager 1 moved at a constant rate for that entire time)

HINT: Rate x Time = Distance

APPROACH # 1-- Break the beast into managable steps:

Rate → Given as 38,100 miles/hour

Time → Given as 34.0 years (so this example is a couple of years old... that's ok, honest)

Distance → To be calculated

Reasoning →

• We know that rate x time = distance.
• The rate is given in miles/hour.  Therefore we must change time from years into hours so we can calculate distance.

Step 1: Put in units only (and ONLY the units)
34.0 years	days	hrs
	yr	days
Notice that we use the units to 'show us the way'.  Each unit type in the numerator (on top) is matched by the same type in the denominator of the next 'track'

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Step 2: Verify that the units cancel and we're left with the units that we want (hrs):
34.0 yrs	days	hrs
	yr	days
We see that the answer will be in hrs, which is what we want -- our confidence is high that our method is accurate

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Step 3: Plug in the appropriate conversion values:
34.0 yrs	365 days	24 hrs
	1 yr	1 days
Verify our conversion factors are accurate and multiply:

-

Step 4: Multiply across the top row:
34.0 yrs	365 days	24 hrs	297,840 hrs
	1 yr	1 days
We still need to sig fig-ize our answer: 3 sig figs in our data, so we need 3 sig figs in our answer: 298,000 hrs or 2.98 x 105 hrs

LET'S RECAP:

Rate → Given as 38,100 miles/hour

Time → Calculated to be 298,000 hrs

Distance → To be calculated next:

38,100 miles	298,000 hrs	→	1.13538 x 1010 miles
1 hr	1

Last step: Convert from miles to hectos - let's put in units first:

1.13538 x 1010 miles	ft	in	cm	m	hm	→	hm
	mile	ft	in	cm	m
Our units cancel appropriately and we are left with hm, so we are clearly set up correctly.

-Now let's plug in the conversion values:((Notice that I have color-coded the units to make the canceling easier to follow)

1.13538 x 1010 miles	5280 ft	12 in	2.54 cm	1 m	1 hm	→	1.83 x 1011 hm
	1 mile	1 ft	1 in	100 cm	100 m
In words: 183 billion hectometers or 18.3 billion kilometers away from the Earth after 34 years of traveling at 30 x the speed of a bullet!

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APPROACH # 2 - BRUTE FORCE - do it all at once!

Feeling adventurous? Howzabout doing it all in 1 RR track???

Note that I have color-coded the units to make the canceling easier to follow

38,100 mi	5280 ft	12 in	2.54 cm	1 m	1 hm	34.0 yrs	365 days	24 hrs	→	1.83 x 1011 hm
1 hr	1 mile	1 ft	1 in	100 cm	100 m	--	1 yr	1 day
given speed	Convert from miles/hr into hm/hr					convert 34.0 yrs into hrs and multiply
The last section is (to me at least) the most confusing... see if you can work through those steps -- MAKE them make sense.