Question 916078
Let {{{ s }}} = Mater's speed in mi/hr
{{{ s + 18 }}} = lightening McQueen's speed in mi/hr
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Start  stopwatch when L.M. leaves
Let {{{ d }}} = distance in miles  L.M travels
until he catches Mater
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Mater's head start is:
{{{ d[1] = s*2 }}}
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Equation for Mater:
(1) {{{ d - s*2 = s*5 }}}
Equation for L.M.
(2) {{{ d = ( s + 18 )*5 }}}
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(2) {{{ d = 5s + 90 }}}
Substitute (2) into (1)
(1) {{{ 5s + 90 - 2s = 5s }}}
(1) {{{ 2s = 90 }}}
(1) {{{ s = 45 }}}
and
{{{ s + 18 = 63 }}}
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L.M. traveled:
(1) {{{ d - 2s = 5s }}}
(1) {{{ d = 7s }}}
(1) {{{ d = 7*45 }}}
(1) {{{ d = 315 }}}
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Mater traveled:
{{{ d[1] + 225 }}}
{{{ 90 + 225 = 315 }}}
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L.M. traveled 315 mi
Mater traveled 315 mi
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check:
(1) {{{ d - s*2 = s*5 }}}
(1) {{{ d = 7s }}}
(1) {{{ 315 = 7*45 }}}
(1) {{{ 315 = 315 }}}
and
(2) {{{ 315 = ( s + 18 )*5 }}}
(2) {{{ 315 = ( 45 + 18 )*5 }}}
(2) {{{ 315 = 63*5 }}}
(2) {{{ 315 = 315 }}}
OK