Question 1089679
Find convict's headstart in miles
{{{ d[1] = 10*12 }}}
{{{ d[1] = 120 }}} mi
----------------------
Let {{{ d }}} = distance the guard travels until
the guard catches convict
Let {{{ t }}} = time in hrs until the guard catches
up with the convict
-------------------------------------------
Equation for the convict:
(1) {{{ d - d[1] = 10t }}}
Equation for the guard:
(2) {{{ d = 70t }}}
-----------------------
(1) {{{ d = 10t + 120 }}}
Plug (2) into (1)
(1) {{{ 70t = 10t + 120 }}}
(1) {{{ 60t = 120 }}}
(1) {{{ t = 2 }}}
and
(2) {{{ d = 70*2 }}}
(2) {{{ d = 140 }}}
The convict is caught 140 mi from the prison
----------------
check:
(1) {{{ d - d[1] = 10t }}}
(1) {{{ d - d[1] = 10*2 }}}
(1) {{{ d - 120 = 20 }}}
(1) {{{ d = 140 }}}
OK