SOLUTION: The elevator in the Washington Monument takes 75 seconds to travel 500 feet to the top floor. What is the speed of the elevator in miles per hour? Give your answer to the two signi

Question 95216: The elevator in the Washington Monument takes 75 seconds to travel 500 feet to the top floor. What is the speed of the elevator in miles per hour? Give your answer to the two significant digits.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To convert this to miles/hour you need a couple of conversion factors.
.
First you need to know that the quantity 5280 feet is equal to 1 mile
.
Then you need to know that 60 sec is equivalent to 1 minute
.
Finally you need to know that 60 minutes is equal to 1 hour
.
You use these conversion factors to multiply the original problem you were given and this
will convert that given to miles/hour.
.
The trick is to recognize that you want to cancel the feet out and replace it with miles.
Notice that the units of feet are in the numerator. Therefore, you need the conversion
factor to have feet in the denominator. So the conversion factor we will use is:
.

.
And we will multiply that times
.
Next, we need to get rid of the seconds in the denominator of the original given problem.
To do that we need to have seconds in the numerator. That means that we need to have our
first conversion of time be in the form . That will get rid of the
secs but will leave you with min in the denominator. To get rid of the min in the denominator
we need to have units of min in the numerator. So our next conversion factor is:
.
.
.
Now we are ready to multiply the original given by the three conversion factors. In algebraic
form this becomes:
.

.
Notice the pattern of how the units cancel:
.

.
Notice that the only units that are left are miles in the numerator and hrs in the denominator.
Therefore, all we have to do is multiply the numbers in the numerator and divide by the
numbers in the denominator and we will have the answer in miles per hour.
.
The multiplication of the numbers is:
.

.
So the answer is 4.54545454 miles per hour and you can round this off to the two significant
digits as required by the problem.
.
Hope this shows you a logical approach to making the conversion factors work for you. By
ensuring that the units cancel to leave you with the units you need for the answer you
will be helping to make sure the conversion factors are not accidentally inverted so
that you don't build in a multiplication mistake.
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