Question 1066151
Let their speeds = {{{ 4x }}} and {{{ 5x }}}
Let the time for the slow car = {{{ t }}}
{{{ t - 1/2 }}} = the time for the fast car
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Slow car:
(1) {{{ 160 = 4x*t }}}
(2) {{{ 160 = 5x*( t - 1/2 ) }}}
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(1) {{{ t = 160/(4x) }}}
(1) {{{ t = 40/x }}}
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(2) {{{ 160 = 5x*( 40/x - 1/2 ) }}}
(2) {{{ 160 = 200 - (5/2)*x }}}
(2) {{{ 320 = 400 - 5x }}}
(2) {{{ 5x = 80 }}}
(2) {{{ x = 16 }}}
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{{{ 4x = 4*16 }}}
{{{ 4x = 64 }}}
and
{{{ 5x = 5*16 }}}
{{{ 5x = 80 }}}
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The slow car's speed is 64 mi/hr
The fast car's speed is 80 mi/hr
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check:
(1) {{{ 160 = 4x*t }}}
(1) {{{ 160 = 64t }}}
(1) {{{ t = 2.5 }}}
and
(2) {{{ 160 = 5x*( t - 1/2 ) }}}
(2) {{{ 160 = 80*( t - .5 ) }}}
(2) {{{ 160 = 80t - 40 }}}
(2) {{{ 80t = 200 }}}
(2) {{{ t = 2.5 }}}
OK