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