Question 458514
Is the 804 meters or miles? I assume it's miles.
If not, just do a conversion.
The key is: how much of a head start does your son have?
{{{ 5 }}} sec = {{{ 5/3600 }}} hrs
In 5 seconds at 6 mi/hr, he goes
{{{ d = r*t }}}
{{{ d = 6*(5/3600) }}} mi
{{{ d = .00833 }}} mi head start
Now you start a stopwatch when you are released.
Your equation is:
(1) {{{ d[f] = 7t }}} (t is in hours)
Your Son's equation is:
(2) {{{ d[s] = 6t  }}} ( you both will have the same t now)
and
(3) {{{ d[f] = d[s] + .00833 }}}
You have 3 equations and 3 unknowns, so it's solvable
Substitute (1) and (2) in (3)
(3) {{{ 7t = 6t + .00833 }}}
(3) {{{ t = .00833 }}} hrs
Now convert to seconds:
{{{ .00833 }}} hrs x {{{ 3600 }}} sec/hr = {{{ 30 }}} sec
It will take you 30 sec to pass your son
------------------------------
You will have gone
{{{ d[f] = 7*.00833 }}}
{{{ d[f] = .05831 }}} mi
That is {{{ .05831*5280 = 307.88 }}} ft