SOLUTION: Perform conversion 150 ft/sec = __

SOLUTION: Perform conversion 150 ft/sec = ___ mile/hr

Question 107270: Perform conversion
150 ft/sec = ___ mile/hr
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given 150 ft/second. To convert this to mile/hr you can use the following chain of ratios:
.
AMP Parsing Error of [((150*ft)/(1*sec))*((60*sec)/(1*min))*((60*min)/(1*hr))*((1*mile)/(5280*ft)))]: Invalid function '))*((60*sec)/(1*min))*((60*min)/(1*hr))*((1*mile)/(5280*ft)))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. .
.
The conversion ratios are arranged so that all the units cancel out except for miles in
the numerator and hours in the denominator. Notice that in each of the three conversion
ratios the number of units in its numerator is equivalent to the number of units in its
denominator. For example the numerator of 60 seconds is equivalent to the denominator
of 1 minute.
.
Once you get the hang of arranging the conversion ratios so their units cancel, the method
for working these problems is quite straightforward.
.
To work this problem, let's start canceling units to make sure that we go from feet per
second to miles per hour:
.
first the units of seconds cancel out so "sec" disappears:
AMP Parsing Error of [((150*ft)/(1*cross(sec)))*((60*cross(sec))/(1*min))*((60*min)/(1*hr))*((1*mile)/(5280*ft)))]: Invalid function ')))*((60*cross(sec))/(1*min))*((60*min)/(1*hr))*((1*mile)/(5280*ft)))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. .
.
next the units of minutes cancel out so "min" also disappears:

.
then the units of feet cancel out so "ft" disappears:

.
At this point, the only units that are left are miles divided by hours ... which is the
"miles per hour" that we are looking for. So all you have to do is multiply all the numbers
in the numerator, then multiply all the numbers in the denominator:

.
The numerator is and this product is and the
denominator is and this product is
.
So the answer comes from:
.
and when you divide 540000 by 5280 you get the final answer of:
.

.
150 feet per second converts to 102.2727273 miles per hour
.
Hope this gives you some insight into the methods by which you can convert from one set
of units to another. The cancellation of units is a way to make sure you get the numerators
and denominators of the conversion factors right-side-up.
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