Question 1046861
What is Mr Abou's head start in km ?
{{{ d[1] = 60*1 }}}
{{{ d[1] = 60 }}} km
----------------------
Start a stopwatch when Mr Collins leaves
Let {{{ t }}} = the time on the stopwatch in hrs
when Mr Collins catches up with Mr Abou
Let {{{ d }}} = distance in km that Mr Collins
travels until he catches up with Mr Abou
----------------------------------------
Mr Collins equation:
(1) {{{ d = 100t }}}
Mr Abou's equation:
(2) {{{ d - 60 = 60t }}}
--------------------
Substitute (1) into (2)
(2) {{{ 100t - 60 = 60t }}}
(2) {{{ 40t = 60 }}}
(2) {{{ t = 1.5 }}}
In 1 hr 30 min, Mr Collins catches up
with Mr Abou
------------------
check:
(1) {{{ d = 100t }}}
(1) {{{ d = 100*1.5 }}}
(1) {{{ d = 150 }}} km
and
(2) {{{ d - 60 = 60t }}}
(2) {{{ d - 60 = 60*1.5 }}}
(2) {{{ d = 60 + 90 }}}
(2) {{{ d = 150 }}} km
OK