Question 372100
how to find whether 10 mi/h is faster than 15 ft/s
<pre>
Start with {{{expr(10mi/h)}}}

To cancel away the miles and bring in feet multiply by the unit
fraction{{{5280ft/(1mi)}}}

{{{expr(10mi/h)expr(5280ft/(1mi))}}}

To cancel away the hours and bring in minutes multiply by the unit
fraction{{{1h/(60m)}}}

{{{expr(10mi/h)expr(5280ft/(1mi))expr(1h/(60min))}}}

To cancel away the minutes and bring in seconds multiply by the unit
fraction{{{1min/(60s)}}}

{{{expr(10mi/h)expr(5280ft/(1mi))expr(1h/(60min))expr(1min/(60s))}}}.

Cancel the miles:

{{{expr(10cross(mi)/h)expr(5280ft/(1cross(mi)))expr(1h/(60min))expr(1min/(60s))}}}.

Cancel the hours:

{{{expr(10cross(mi)/cross(h))expr(5280ft/(1cross(mi)))expr(1cross(h)/(60min))expr(1min/(60s))}}}.

Cancel the minutess:

{{{expr(10cross(mi)/cross(h))expr(5280ft/(1cross(mi)))expr(1cross(h)/(60cross(min)))expr(1cross(min)/(60s))}}}.

All that's left is

{{{expr((10*5280)/(60*60))}}}{{{expr(ft/s)}}}

{{{52800/3600}}}{{{ft/s}}}

{{{44/3}}}{{{ft/s}}}

And {{{15}}}{{{ft/s}}} = {{{45/3}}}{{{ft/s}}}

So {{{15}}}{{{ft/s}}} is slightly faster than {{{10}}}{{{mi/h}}}

Edwin</pre>