Function for converting mph to min/mile
anyone have a good function for converting mph to min/mile. I can see that graph starting at say 60min/mile for 1 mpg decreases by half for every doubling of input, I.e. 2mph -> 30min/mile. 4pmh -> 15min/mile.
But for some reason I can't wrap my head around how to come up with a function for this.
The reason I want to know is because I'm taking a numerical computation class and we are thinking about how computers represent numbers and how there are errors when truncating binary numbers.
An example I found of this in the real world is that on my treadmill machine, if it starts at 2mph and I add increments of 0.1mph until I reach 6mph, the pace always is calculated to 9:59min/mile instead of 10min/mile. If anyone could explain in further detail that second part, that would be really cool, but I bet if I just got a function I could figure out why the computer is calculating that.
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$\begingroup$You can look up dimensional analysis to get a feel for these types of problems.
First, let's convert mph to miles per minute. $$\frac{x\text{ miles}}{1\text{ hour}}\times\frac{1\text{ hour}}{60\text{ minutes}}=\frac{x}{60}\text{miles per minute}$$
Then to get minutes per mile, we invert that. So x mph = $\frac{60}{x}$ minutes per mile.
$\endgroup$ $\begingroup$Swap velocity into its reciprocal: $$v=x\frac{\text{miles}}{\text{hour}}\implies\frac{1}{v}=\frac{1}{x}\frac{\text{hour}}{\text{miles}}$$ Expand the units as desired: $$\frac{1}{v}=\frac{1}{x}\frac{\text{hour}}{\text{miles}}=\frac{1}{x}\frac{60\text{min}}{\text{miles}}$$
$\endgroup$ $\begingroup$So your numerical function would be: $x\mapsto\frac{1}{x}60$
First convert $s$ mph to ${1 \over s}$ hours per mile.
Since 1 hour per mile is 60 mins. per mile, we see that $s$ mph becomes ${60 \over s}$ mins. per mile.
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