Question 624496
Let {{{ t }}} = the time for both trains
Let {{{ s }}} = the speed of the passenger train in km/hr
{{{ s - 14 }}} = the speed of the freight train in km/hr
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Equation for passenger train:
(1) {{{ 400 = s*t }}}
Equation for freight train:
(2) {{{ 330 = ( s - 14 )*t }}}
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(2) {{{ 330 = s*t - 14t }}}
Substitute (1) into (2)
(2) {{{ 330 = 400 - 14t }}}
(2) {{{ 14t = 400 - 330 }}}
(2) {{{ 14t = 70 }}}
(2) {{{ t = 5 }}}
and
(1) {{{ 400 = s*5 }}}
(1) {{{ s = 400/5 }}}
(1) {{{ s = 80 }}}
{{{ s - 14 = 66 }}}
The speed of the freight train is 66 km/hr
check:
(2) {{{ 330 = ( 80 - 14 )*5 }}}
(2) {{{ 330 = 66*5 }}}
(2) {{{ 330 = 330 }}}
OK