Question 1047445
Let {{{ t }}} = time in hrs for both trains
Let {{{ s }}} = speed of the passenger train in mi/hr
{{{ s - 5 }}} = speed of the freight train in mi/hr
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Equation for passenger train:
(1) {{{ 100 = s*t }}}
Equation for freight train:
(2) {{{ 80 = ( s - 5 )*t }}}
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(1) {{{ t = 100/s }}}
and
(2) {{{ 80 = ( s-5 )*( 100/s ) }}}
(2) {{{ 80s = 100s - 500 }}}
(2) {{{ 20s = 500 }}}
(2) {{{ s = 25 }}} mi/hr
and
{{{ s - 5 = 20 }}}
The rate of the passenger train is 25 mi/hr
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check:
(1) {{{ 100 = s*t }}}
(1) {{{ 100 = 25*t }}}
(1) {{{ t = 4 }}} hrs
and
(2) {{{ 80 = ( s - 5 )*t }}}
(2) {{{ 80 = ( 25 - 5 )*t }}}
(2) {{{ 80 = 20t }}}
(2) {{{ t = 4 }}} hrs
OK