SOLUTION: I hope you can help me. I just went back to school and I am having so much trouble with the math (I had to start college in the "stupid math" class, and I'm STILL having trouble!)

Question 167301: I hope you can help me. I just went back to school and I am having so much trouble with the math (I had to start college in the "stupid math" class, and I'm STILL having trouble!). Unfortunately my math professor is not very good at explaining things. He's very nice, but he's very old, and when he's putting a problem on the board, he sometimes gets confused and gets the wrong answer, which then confuses me even more! I need to know about unit multipliers. How do you know which measurement goes where (top or bottom of fraction)? I had a homework question (which I got wrong; I know the answer, but I still cannot find out how to get that answer.
Convert 44 feet per second to miles per hour.
The answer is 38 mph, but I have absolutely no idea how they came up with that answer. I've been working on this problem for over an hour. Thank you so much for your help.
DT
Found 3 solutions by gonzo, scott8148, ptaylor:
Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!
unit multipliers always have the same measure on opposite sides of the dividing line.
example:
60 seconds = 1 minute is the equation you start with to create the unit multiplier as required.
if you have x per second, you would multiply by 60 seconds per minute.
in equation form, this works out to be:

as you can see the seconds are on opposite sides of the dividing line.
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in your problem you have:
44 feet per seconds = how many miles per hour.
equations you need are:
1 minutes = 60 seconds
1 hour = 60 minutes
1 mile = 5280 feet
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if we work this out piece by piece, we get the following:
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first we convert from feet per second to feet per minute.

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next we convert from feet per minute to feet per hour.

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next we want to convert from feet to miles.

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the common measure is always on opposite sides of the dividing line.
means the same thing as 30 miles per hour.
you create the fraction that way.
44 feet per second = etc.
always start with the equality, like 1 minute = 60 seconds, and then decide which unit multiplier you want to create from that.
hope this helps.
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Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
the easiest way is to think about which unit is smaller or larger
__ with fractional quantities (like ft/sec or dollars/gal), do the numerator and denominator seperately

miles are larger than feet, so there will be fewer for the same distance
__ this means multiplying feet by a fraction LESS than one

the same is true for hours and seconds
__ but in this case, the seconds are in the denominator
__ so a smaller denominator means a larger fraction

44ft/sec __ there are 60 sec in a min, so you can go 60 times as far as in a sec
__ 44ft/sec = 2640ft/min
__ there are 60 min in an hr, so you can go 60 times as far as in a min
__ 2640ft/sec = 158400ft/hr

there are 5280ft in a mi __ 158400ft/hr / 5280ft/mi = 30mi/hr

you can also use "conversion factors" incorporating units
__ the units cancel like variables in multiplying fractions

AMP Parsing Error of [(44ft/sec)*(60sec/1min)*(60min/1hr)*(1mi/5280ft)=30mi/hr]: Invalid function ')*(60\sec/1\min)*(60\min/1\hr)*(1\mi/5280\ft)=30\mi/hr': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. .
Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
1 ft=(1/5280)mi
44 ft=(44/5280)mi
1 sec=(1/60)*(1/60)=(1/3600)hr
(1 sec=1/60 min and 1 min=1/60 hr, so 1 sec=1/3600 hr)
Now lets put it togethr
44 ft/sec=(44/5280)mi/(1/3600)hr
(44/5280)/(1/3600)=(multiply numerator and denominator by (3600/1) to get rid of the complex fraction:
(44/5280)*(3600/1)/(1/3600)*(3600/1) mi/hr=
(44*3600)/5280 mi/hr=
158400/5280 mi/hr= 30 mi/hr
CK my Math----I didn't come up with 38 mi/hr but hopefully you see the approach.
P.S. I think that 30 mi/hr is correct.
Hope this helps---ptaylor

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