Question 1200497
<font color=black size=3>
1 mile = 5280 ft
1 hour = 60 min
1 min = 60 sec


Converting from mph to ft per sec
{{{
matrix(1,2,20,"mph")
=
(matrix(1,2,20,"mi")/matrix(1,2,1,"hr"))
*
(matrix(1,2,5280,"ft")/matrix(1,2,1,"mi"))
*
(matrix(1,2,1,"hr")/matrix(1,2,60,"min"))
*
(matrix(1,2,1,"min")/matrix(1,2,60,"sec"))
}}}


{{{
matrix(1,2,20,"mph")
=
(matrix(1,2,20,cross("mi"))/matrix(1,2,1,"hr"))
*
(matrix(1,2,5280,"ft")/matrix(1,2,1,cross("mi")))
*
(matrix(1,2,1,"hr")/matrix(1,2,60,"min"))
*
(matrix(1,2,1,"min")/matrix(1,2,60,"sec"))
}}} "miles" units cancel


{{{
matrix(1,2,20,"mph")
=
(matrix(1,2,20,"")/matrix(1,2,1,cross("hr")))
*
(matrix(1,2,5280,"ft")/matrix(1,2,1,""))
*
(matrix(1,2,1,cross("hr"))/matrix(1,2,60,"min"))
*
(matrix(1,2,1,"min")/matrix(1,2,60,"sec"))
}}} "hours" units cancel



{{{
matrix(1,2,20,"mph")
=
(matrix(1,2,20,"")/matrix(1,2,1,""))
*
(matrix(1,2,5280,"ft")/matrix(1,2,1,""))
*
(matrix(1,2,1,"")/matrix(1,2,60,cross("min")))
*
(matrix(1,2,1,cross("min"))/matrix(1,2,60,"sec"))
}}} "minutes" units cancel
The only thing left will be "ft" up top and "sec" down below
That gives the speed unit ft/sec aka "feet per second", often abbreviated to fps.


Let's finish up the calculation
{{{
matrix(1,2,20,"mph")
=
(matrix(1,2,20,"")/matrix(1,2,1,""))
*
(matrix(1,2,5280,"ft")/matrix(1,2,1,""))
*
(matrix(1,2,1,"")/matrix(1,2,60,""))
*
(matrix(1,2,1,"")/matrix(1,2,60,"sec"))
}}}


{{{
matrix(1,2,20,"mph")
=
matrix(1,2,(20*5280*1*1)/(1*1*60*60),"ft/sec")
}}}


{{{
matrix(1,2,20,"mph")
=
matrix(1,2,(105600)/(3600),"ft/sec")
}}}


{{{
matrix(1,2,20,"mph")
=
matrix(1,2,29.33333333,"ft/sec")
}}} which is approximate; the '3's go on forever.


The person biking at 20 mph is moving at roughly 29.33333333 ft/sec


distance = rate*time
distance = (29.33333333 ft/sec)*(30 sec)
distance = 879.9999999
distance = <font color=red>880 feet</font> is the final answer.


------------------------------------------------


Another approach:


1 hour = 60 min
1 min = 60 sec
Those two equations tell us that
1 hour = 60*60 = 3600 sec


Meaning that 1 second is 1/3600 of an hour.
30 seconds is 30*(1/3600) = 30/3600 = 1/120 of an hour.


distance = rate*time
distance = (20 mph)*(1/120 of an hour)
distance = 20/120 miles
distance = 1/6 of a mile.



Then,
1 mile = 5280 ft
(1/6)*1 mile = (1/6)*5280 ft
1/6 of a mile = <font color=red>880 feet</font>



------------------------------------------------



Answer: <font color=red>880 feet</font>
</font>