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We start with feet per hour or ft/hr.
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\n" ); document.write( "We need to cancel ft and replace it with yds. We know there are 3 feet per 1 yd. But since
\n" ); document.write( "we need ft in the denominator to cancel out the ft in the numerator of the dimension ft/hr,
\n" ); document.write( "so the ratio we need is (1 yd)/(3 ft). Insert this factor to get:
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\n" ); document.write( "(32 ft)/(1 hr) * (1 yd)/(3 ft)
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\n" ); document.write( "Next we know that there are 24 hours per 1 day. We need the hours in the numerator so that it
\n" ); document.write( "cancels the hour in the denominator of ft/hr. So our ratio of (24 hr)/(1 day) will work.
\n" ); document.write( "Insert this factor to get:
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\n" ); document.write( "(32 ft)/(1 hr) * (1 yd)/(3 ft) * (24 hr)/(1 day)
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\n" ); document.write( "Now look to the denominators and numerators. The ft with the 32 is in the numerator
\n" ); document.write( "and it will cancel with the ft with the 3 which is in the denominator. And the hr in the denominator
\n" ); document.write( "with the 1 will cancel with the hr with the 24 in the numerator. The only dimensions
\n" ); document.write( "remaining after those cancellations are yd in the numerator and day in the denominator and
\n" ); document.write( "this is what we are looking for.
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\n" ); document.write( "Now all we have to do is multiply and divide the numbers. In the numerators the product is:
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\n" ); document.write( "32*1*24
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\n" ); document.write( "and multiplying this out results in an answer of 768
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\n" ); document.write( "And the corresponding multiplication of the numbers in the denominator is:
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\n" ); document.write( "1*3*1
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\n" ); document.write( "And this result is 3
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\n" ); document.write( "So our answer is (768/3) yd/day and after the division by 3 it becomes:
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\n" ); document.write( "256 yd/day
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\n" ); document.write( "Not too bad. Just a little trouble to keep things straight. And checking this seems to
\n" ); document.write( "be a little more straightforward. If you go 256 yards in a day, how many feet did you
\n" ); document.write( "go in that day ... just multiply 3 times 256 to get 768 feet per day. And if you went
\n" ); document.write( "768 feet in a day, how many feet did you go each hour. Just divide by 24 to get 32 ft per hour.
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\n" ); document.write( "Works!
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\n" ); document.write( "Hope this helps. Just make sure you get your ratios correct. Then just put the numerator
\n" ); document.write( "and denominator in the correct arrangement so that the dimensions will cancel with those
\n" ); document.write( "of preceding terms when you multiply things out.
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\n" ); document.write( "Hope this helps. \n" ); document.write( "