Question 797543
Let {{{ s }}} = Ryan's average speed in km/hr
{{{ s*3 }}} = Ryan's head start in km
{{{ s + 42 }}} = Gabriella's average speed in km/hr
Let {{{ d }}} = the distance in km  Gabriella travels in 2 hrs
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Start a stop watch when Gabriella leaves and stop it in 2 hrs
Ryan's equation:
(1) {{{ d - s*3 = s*2 }}}
Gabriella's equation:
(2) {{{ d = ( s + 42 )*2 }}}
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substitute (2) into (1)
(1) {{{ ( s + 42 )*2 - 3s = s*2 }}}
(1) {{{ 2s + 84 - 3s = 2s }}}
(1) {{{ -s + 84 = 2s }}}
(1) {{{ 3s = 84 }}}
(1) {{{ s = 28 }}}
Ryan's average speed is 28 km/hr
check:
(1) {{{ d - 3s = s*2 }}}
(1) {{{ d - 3*28 = 28*2 }}}
(1) {{{ d - 84 = 56 }}}
(1) {{{ d = 140 }}}
and
(2) {{{ d = ( s + 42 )*2 }}}
(2) {{{ d = ( 28 + 42 )*2 }}}
(2) {{{ d = 70*2 }}}
(2) {{{ d = 140 }}}
OK