Question 771266
Let {{{ t }}} = Jimmy's time in hrs to travel 480 mi
{{{ t/4 }}} = Ronald's time to travel 360 mi
Let {{{ s }}} = Jimmy's speed in mi/hr
{{{ s + 60 }}} = Ronald's speed in mi/hr
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Jimmy's equation:
(1) {{{ 480 = s*t }}}
Ronald's equation:
(2) {{{ 360 = ( s + 60 )*( t/4 ) }}}
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(2) {{{ 360 = ( s*t )/4 + 15t }}}
(2) {{{ 360 = t*( s/4 + 15 ) }}}
and
(1) {{{ t = 480/s }}}
Substitute (1) into (2)
(2) {{{ 360 = ( 480/s )*( s/4 + 15 ) }}}
(2) {{{ 360 = 480/4 + ( 480*15 )/ s ) }}}
(2) {{{ 360 = 120 + 7200/s }}}
(2) {{{ 240 = 7200/s }}}
(2) {{{ s = 7200/240 }}}
(2) {{{ s = 30 }}}
{{{ s + 60 = 90 }}}
and
(1) {{{ 480 = s*t }}}
(1) {{{ 480 = 30*t }}}
(1) {{{ t = 16 }}}
{{{ t/4 = 4 }}}
Jimmy's speed is 30 mi/hr
His time is 16 hrs
Ronald's speed is 90 mi/hr
His time is 4 hrs
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check:
(2) {{{ 360 = ( s + 60 )*( t/4 ) }}}
(2) {{{ 360 = ( 30 + 60 )*( 16/4 ) }}}
(2) {{{ 360 = 90*4 }}}
(2) {{{ 360 = 360 }}}
OK