What is a distance an object went through at the speed of 14hm/min for 6 hours?
I am having problems with conversions.
First, I tried passing 14hm/min to m/s. I did it alright. But now I am unsure. Do I multiply it by 6 hours and I'm done?
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You can leave the 14hm/min just as it is, if you like. Convert the 6 hours to how many minutes there are in 6 hours, 6 hours times 60 minutes per hour = 360 minutes. The comments on your Question are beside the point, hm could be half-meters, hectometers, whatever, ... — if one travels 14 “hm”s in 1 minute, then one travels 360 times 14 “hm”s in 360 minutes. You could also convert the 14 hm/min into hm/hour, $60\times 14$ hm/hour, then multiply that by the number of hours. It's possible to keep track of the units quite nicely by arranging everything on two lines, $$\frac{14\ {\rm hm}}{{\rm minute}}\times\frac{60\ {\rm minute}}{{\rm hour}}\times 6\ {\rm hour} = 14\times 60\times 6 {\rm hm}.$$ The different units all cancel, leaving behind the conversion factors. If you do this methodically every time then this kind of conversion, and harder ones, will become second nature. |
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Peter Morgan's answer is the most straightforward. It doesn't matter what an 'hm' is. If you go 14 of them in one minute, then you go: (14hm/min) * (60 min/hr) * (6 hr) = (14 * 360) hm = 5040 hm in 6 hours. The technique you need to master, in unit conversion, is unit cancellation. Notice, in the equation above, that 'min' in the numerator of the first term cancels out 'min' in the denominator in the second. Likewise for 'hr' in the second and third terms. All that is left is 'hm' and a little math. Now, if you want to convert 'hm' to meters, you'll need to tell us what an 'hm' is. |
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The answer to this question is yes, but... Remember that when we multiple quantities together it is important that they are all in standard (SI) units. This will make it easier to keep track of what units your answer will be in. The question is one that concerns speed ($s$), distance ($d$) and time ($t$). The equation relating them is: $$ s=d/t$$ Rearranging this to get the distance as the subject (as per your question) gives: $$ d=st$$ Like I said- once you've converted all the values to SI units, it's merely a case of putting the values into your calculator and seeing what you get. |
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