Question 763744
Convert {{{ 10 }}} min to hours
{{{ 10/60 }}} hrs
--------------
What is the robbers head start in miles?
{{{ d[1] = 12*( 10/60 ) }}}
{{{ d[1] = 2 }}} mi
---------------
Start a stopwatch when the marshall leaves
Let {{{ t }}} = time on stopwatch when he catches robber
Let {{{ d }}} = distance in miles that Marshall has to go
until he catches robber
---------------
Robber's equation:
(1) {{{ d - 2 = 12t }}}
Marshall's equation:
(2) {{{ d = 16t }}}
--------------
Substitute (2) into (1)
(1) {{{ 16t - 2 = 12t }}}
(1) {{{ 4t = 2 }}}
(1) {{{ t = 1/2 }}}
the marshall catches robber in a half-hour
check:
(2) {{{ d = 16t }}}
(2) {{{ d = 16*.5 }}}
(2) {{{ d = 8 }}}
and
(1) {{{ d - 2 = 12*.5 }}}
(1) {{{ d = 2 + 6 }}}
(1) {{{ d = 8 }}}
OK