Question 920808
Let {{{ s }}} = Ryan's average speed
What is Ryan's head start in km?
{{{ d[1] = s*3 }}}
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Start a stopwatch when Gabriella leaves
Stop the stopwatch {{{2}}} hrs later when
she catches up with Ryan
Let {{{ d }}} = the distance in km that
Gabriella travels until she catches him
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Ryan's equation:
(1) {{{ d - 3s = s*2 }}}
Gabriella's equation:
(2) {{{ d = ( s + 42 )*2 }}}
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(1) {{{ d = 2s + 3s }}}
(1) {{{ d = 5s }}}
Substitute (1) into (2)
(2) {{{ 5s = 2s + 84 }}}
(2) {{{ 3s = 84 }}}
(2) {{{ s = 28  }}}
Ryan's average speed is 28 km/hr
check:
{{{ s + 42 = 28 + 42 }}}
{{{ s + 42 = 70 }}}
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(1) {{{ d = 5*28 }}}
(1) {{{ d = 140 }}}
and
(2) {{{ d = ( s + 42 )*2 }}}
(2) {{{ d = 70*2 }}}
(2) {{{ d = 140 }}}
OK